Finite Group Databasebeta

← #14238634

Subgroups — #14238634

Order 1792.

2234 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#546C211yesmaximal, characteristic
2#11742834C211yesmaximal, characteristic, complemented
3#11741529C212yesmaximal, complemented
4C2×#89990C212yesmaximal, complemented
5#11740951C218yesmaximal, complemented
6#11740943C218yesmaximal, complemented
7#11740394C212yesmaximal, complemented
8#11740186C212yesmaximal, complemented
9#11740076C212yesmaximal, complemented
10#11739760C212yesmaximal, complemented
11#11739747C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C7×#546—24no—
15C7×#546C2218yes—
16C2×C7×#124C2211yescharacteristic
17C2×C7×#123—21no—
18C2×C7×C22⋊Q8C2211yescharacteristic
19C2×C7×#121—21no—
20C2×C7×#121C2211yescharacteristic
21C2×C7×#120—21no—
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C22×C7×C22⋊C4—21no—
25C2×#6514C2214yescomplemented
26#90489—21no—
27C22×#1142C2214yescomplemented
28C2×#6487C2212yes—
29C2×#6487C2212yescomplemented
30#90234C2214yescomplemented
31#90230—24no—
32D4×Dic14C2214yescomplemented
33#90191—21no—
34#90174—21no—
35#90174—21no—
36#90161C2212yescomplemented
37#90011C2218yescomplemented
38#90004C2214yescomplemented
39#90000C2214yescomplemented
40#89990C2214yes—
41#89990C2214yes—
42#89990C2218yescomplemented
43C2×#6406C2214yescomplemented
44#89979C2212yescomplemented
45C2×C22⋊(C7⋊C8)C2212yes—
46#89832C2214yescomplemented
47#89827C2214yescomplemented
48#89826C2218yescomplemented
49#89823C2218yescomplemented
50#89822C2214yescomplemented
51#89816C2214yescomplemented
52#89814C2218yescomplemented
53#89812C2214yescomplemented
54#89805C2214yescomplemented
55#89791C2214yescomplemented
56#89790C2218yescomplemented
57#89783C2218yescomplemented
58#89779C2214yescomplemented
59#89742C2214yescomplemented
60#89698C2212yescomplemented
61#61570—71nomaximal, Sylow
62C25×C7—21no—
63C2×C7×#41—22no—
64C2×C7×#41—44no—
65C2×C7×#41C2314yes—
66C22×C7×Q8C2311yescharacteristic
67C22×C7×D4—21no—
68C22×C7×D4—21no—
69C22×C7×D4—21no—
70C22×C7×D4—22no—
71C22×C7×D4—44no—
72C22×C7×D4D411yescharacteristic
73C22×C7×D4C2311yescharacteristic
74C22×C7×D4C2314yes—
75C22×C7×D4C2311yescharacteristic
76C23×C4×C7—21no—
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×Dic14C2312yes—
81C22×Dic14C2312yescomplemented
82C7×#124—22no—
83C7×#124C2314yes—
84C7×#123—28no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8C2314yes—
87C7×#121—22no—
88C7×#121—28no—
89C7×#121C2314yes—
90C7×#120—28no—
91C4×C7×D4—22no—
92C4×C7×D4D414yes—
93C4×C7×D4C2314yes—
94C4×C7×D4C2314yes—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4D411yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—28no—
104C2×C7×C22⋊C4D411yescharacteristic
105C2×C7×C22⋊C4D411yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—22no—
109#6514—48no—
110C2×#1144C2318yescomplemented
111D4×Dic7—24no—
112D4×Dic7—24no—
113C2×#1142—48no—
114C2×#1142C2318yes—
115C2×#1142C2318yes—
116#6489—22no—
117C2×C4⋊Dic7C2312yes—
118C2×C4⋊Dic7C2312yescomplemented
119#6487—22no—
120#6487—22no—
121#6487—22no—
122#6487—22no—
123#6487—22no—
124#6487C2314yes—
125#6487C2314yes—
126#6487C2314yescomplemented
127C2×Dic7⋊C4—22no—
128C2×Dic7⋊C4—22no—
129C2×#1136C2314yescomplemented
130C22×C7⋊C8C2314yes—
131#6453—24no—
132#6451—24no—
133#6441—24no—
134#6441—24no—
135#6441—24no—
136#6441—24no—
137#6433—22no—
138#6432C2312yescomplemented
139#6432C2312yescomplemented
140C4×Dic14—22no—
141C4×Dic14C2314yescomplemented
142#6409C2318yescomplemented
143#6406C2318yes—
144#6406C2318yes—
145C22⋊(C7⋊C8)C2314yes—
146C22⋊(C7⋊C8)C2314yes—
147C22⋊(C7⋊C8)C2314yescomplemented
148#6384C2318yescomplemented
149#6381C2318yescomplemented
150C4⋊(C7⋊C8)C2314yescomplemented
151#6377C2314yescomplemented
152#3501—71no—
153C2×#546D711yescharacteristic
154#3314—78no—
155#3266—78no—
156#3215—72no—
157#3193—72no—
158#3189—72no—
159#3110—72no—
160#3007—72no—
161C2×#450—72no—
162#2973—71no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—24no—
166C24×C7—44no—
167C24×C7—44no—
168C24×C7—82no—
169C24×C7C2×D411yescharacteristic
170C24×C7C2×D411yescharacteristic
171C7×#41—28no—
172C7×#41—44no—
173C7×#41—48no—
174C2×C7×Q8—21no—
175C2×C7×Q8—42no—
176C2×C7×Q8C2412yes—
177C2×C7×D4—24no—
178C2×C7×D4—24no—
179C2×C7×D4—28no—
180C2×C7×D4—24no—
181C2×C7×D4—24no—
182C2×C7×D4—21no—
183C2×C7×D4—24no—
184C2×C7×D4—21no—
185C2×C7×D4—44no—
186C2×C7×D4—42no—
187C2×C7×D4—48no—
188C2×C7×D4—44no—
189C2×C7×D4—44no—
190C2×C7×D4—82no—
191C2×C7×D4C2×D414yes—
192C2×C7×D4C2412yes—
193C2×C7×D4C2412yes—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—24no—
197C22×C4×C7—24no—
198C22×C4×C7—42no—
199C22×C4×C7—42no—
200C22×C4×C7—44no—
201C22×C4×C7—82no—
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2411yescharacteristic
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C2×Dic14—22no—
216C2×Dic14—22no—
217C2×Dic14—22no—
218C2×Dic14—44no—
219C2×Dic14—44no—
220C2×Dic14C2414yes—
221C7×C4⋊C4—24no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4C2×D414yes—
224C7×C4⋊C4C2412yes—
225C7×C22⋊C4—24no—
226C7×C22⋊C4—24no—
227C7×C22⋊C4—24no—
228C7×C22⋊C4—24no—
229C7×C22⋊C4—24no—
230C7×C22⋊C4C2×D414yes—
231C7×C22⋊C4C2×D414yes—
232C42×C7C2×D412yes—
233C42×C7C2412yes—
234C22⋊Dic7—24no—
235C22⋊Dic7—24no—
236C22⋊Dic7—24no—
237#1144—48no—
238#1142—216no—
239#1142—48no—
240C4⋊Dic7—22no—
241C4⋊Dic7—22no—
242C4⋊Dic7—22no—
243C4⋊Dic7—22no—
244C4⋊Dic7—22no—
245C4⋊Dic7C2414yes—
246Dic7⋊C4—24no—
247Dic7⋊C4—24no—
248Dic7⋊C4—24no—
249Dic7⋊C4—24no—
250C4×Dic7—24no—
251#1136—44no—
252C2×C7⋊C8—44no—
253C2×C7⋊C8C2418yes—
254C22×#41C2×D711yescharacteristic
255C23×D4C2×D711yescharacteristic
256C2×#137—74no—
257C22×SD16—74no—
258#554—74no—
259#554—144no—
260D4×Q8—74no—
261#546—24no—
262#546C2×D718yes—
263#544—141no—
264#543—141no—
265#543—141no—
266#533—72no—
267C2×#124C2×D711yescharacteristic
268C2×#123—21no—
269C2×C22⋊Q8—72no—
270C2×C22⋊Q8—72no—
271C2×C22⋊Q8C2×D711yescharacteristic
272C2×#121—21no—
273C2×#121C2×D711yescharacteristic
274C2×#120—21no—
275#518—141no—
276C2×C4×D4C2×D711yescharacteristic
277C2×C4×D4C2×D711yescharacteristic
278C22×C22⋊C4—21no—
279#497—74no—
280#489—74no—
281#484—74no—
282#484—74no—
283#480—74no—
284#474—74no—
285#468—78no—
286#467—78no—
287#464—78no—
288#461—74no—
289#452—78no—
290#451—74no—
291#451—74no—
292#450—74no—
293#450—74no—
294#450—78no—
295#448—74no—
296#440—78no—
297#435—78no—
298#432—72no—
299#417—74no—
300C2×#102—74no—
301#407—72no—
302C2×C22⋊C8—72no—
303C23×C7—24no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—48no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7—48no—
317C23×C7—42no—
318C23×C7—84no—
319C23×C7—816no—
320C23×C7#13714yescomplemented
321C23×C7C22×D412yes—
322C23×C7C22×D411yescharacteristic
323C23×C7C22×D412yes—
324C7×Q8—24no—
325C7×Q8—42no—
326C7×D4—24no—
327C7×D4—28no—
328C7×D4—22no—
329C7×D4—24no—
330C7×D4—48no—
331C7×D4—42no—
332C7×D4—48no—
333C7×D4—84no—
334C7×D4H(5,𝔽2)14yes—
335C2×C4×C7—22no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—41no—
346C2×C4×C7—48no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—84no—
350C2×C4×C7C22×D412yes—
351C2×C4×C7C22×D411yescharacteristic
352C2×C4×C7C22×D412yes—
353C2×C4×C7C22×D412yes—
354C2×C4×C7C22×D412yes—
355C2×C4×C7C2511yescharacteristic
356C2×Dic7—24no—
357C2×Dic7—24no—
358C2×Dic7—82no—
359C2×Dic7—82no—
360C2×Dic7—82no—
361C2×Dic7—82no—
362Dic14—28no—
363Dic14—82no—
364Dic14—82no—
365Dic14—82no—
366C7⋊C8—28no—
367C25—21no—
368C2×#41—22no—
369C2×#41—44no—
370C2×#41C22×D714yes—
371C22×Q8—72no—
372C22×Q8—72no—
373C22×Q8C22×D711yescharacteristic
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—22no—
378C22×D4—44no—
379C22×D4C22⋊D711yescharacteristic
380C22×D4C22×D711yescharacteristic
381C22×D4C22×D714yes—
382C22×D4C22×D711yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D711yescharacteristic
387#137—288no—
388C2×Q16—78no—
389C2×SD16—78no—
390C2×SD16—78no—
391C2×SD16—288no—
392C2×M16—74no—
393C22×C8—74no—
394C4⋊Q8—72no—
395C4⋊Q8—72no—
396C4⋊Q8—144no—
397#125—144no—
398#125—142no—
399#124—22no—
400#124C22×D714yes—
401#123—28no—
402C22⋊Q8—22no—
403C22⋊Q8—74no—
404C22⋊Q8—74no—
405C22⋊Q8—74no—
406C22⋊Q8—142no—
407C22⋊Q8—142no—
408C22⋊Q8—142no—
409C22⋊Q8—142no—
410C22⋊Q8—142no—
411C22⋊Q8—144no—
412C22⋊Q8—144no—
413C22⋊Q8—144no—
414C22⋊Q8—144no—
415C22⋊Q8C22×D714yes—
416#121—22no—
417#121—28no—
418#121C22×D714yes—
419#120—28no—
420C4×Q8—74no—
421C4×Q8—142no—
422C4×D4—22no—
423C4×D4—144no—
424C4×D4—144no—
425C4×D4C22⋊D714yes—
426C4×D4C22×D714yes—
427C4×D4C22×D714yes—
428#117—142no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—72no—
431C2×C4⋊C4—72no—
432C2×C4⋊C4—142no—
433C2×C4⋊C4—142no—
434C2×C4⋊C4C22⋊D711yescharacteristic
435C2×C4⋊C4C22×D711yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4C22⋊D711yescharacteristic
445C2×C22⋊C4C22⋊D711yescharacteristic
446C2×C42C22×D711yescharacteristic
447#107—78no—
448C4⋊C8—74no—
449#103—78no—
450#103—78no—
451#102—78no—
452#102—78no—
453C22⋊C8—74no—
454C22⋊C8—74no—
455C22⋊C8—74no—
456#97—74no—
457C22×C7—22no—
458C22×C7—21no—
459C22×C7—22no—
460C22×C7—21no—
461C22×C7—22no—
462C22×C7—22no—
463C22×C7—24no—
464C22×C7—22no—
465C22×C7—44no—
466C22×C7—48no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—82no—
473C22×C7—816no—
474C22×C7—84no—
475C22×C7C2×#13712yes—
476C22×C7C2×#13714yes—
477C22×C7C23×D411yescharacteristic
478C4×C7—22no—
479C4×C7—22no—
480C4×C7—22no—
481C4×C7—21no—
482C4×C7—22no—
483C4×C7—42no—
484C4×C7—42no—
485C4×C7C2×H(5,𝔽2)12yes—
486Dic7—44no—
487Dic7—44no—
488C24—21no—
489C24—21no—
490C24—24no—
491C24—44no—
492C24—44no—
493C24—82no—
494C24C2×C22⋊D711yescharacteristic
495C24C2×C22⋊D711yescharacteristic
496#41—28no—
497#41—44no—
498#41—48no—
499C2×Q8—21no—
500C2×Q8—42no—
501C2×Q8—74no—
502C2×Q8—142no—
503C2×Q8—142no—
504C2×Q8—142no—
505C2×Q8—284no—
506C2×Q8—284no—
507C2×Q8C23×D712yes—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—28no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—24no—
515C2×D4—21no—
516C2×D4—44no—
517C2×D4—42no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—82no—
522C2×D4C2×C22⋊D714yes—
523C2×D4C23×D712yes—
524C2×D4C23×D712yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—82no—
533C22×C4—142no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4C2×C22⋊D711yescharacteristic
538C22×C4C2×C22⋊D711yescharacteristic
539C22×C4C2×C22⋊D711yescharacteristic
540C22×C4C2×C22⋊D711yescharacteristic
541C22×C4C2×C22⋊D712yes—
542C22×C4C2×C22⋊D712yes—
543C22×C4C23×D711yescharacteristic
544C22×C4C23×D712yes—
545C22×C4C23×D712yes—
546Q16—288no—
547SD16—1416no—
548SD16—288no—
549M16—284no—
550C2×C8—78no—
551C2×C8—284no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—74no—
555C4⋊C4—144no—
556C4⋊C4—144no—
557C4⋊C4—144no—
558C4⋊C4—144no—
559C4⋊C4—142no—
560C4⋊C4—142no—
561C4⋊C4—142no—
562C4⋊C4—142no—
563C4⋊C4—142no—
564C4⋊C4C2×C22⋊D714yes—
565C4⋊C4C23×D712yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—144no—
572C22⋊C4—144no—
573C22⋊C4—144no—
574C22⋊C4C2×C22⋊D714yes—
575C22⋊C4C2×C22⋊D714yes—
576C42—144no—
577C42C2×C22⋊D712yes—
578C42C23×D712yes—
579C2×C7—22no—
580C2×C7—24no—
581C2×C7—42no—
582C2×C7—44no—
583C2×C7—82no—
584C2×C7#348411yescharacteristic
585C2×C7C22×#13711yescharacteristic
586C2×C7#358511yescharacteristic
587C23—24no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—48no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—48no—
601C23—42no—
602C23—84no—
603C23—816no—
604C23#651414yescomplemented
605C23C22×C22⋊D712yes—
606C23C22×C22⋊D712yes—
607C23C22×C22⋊D711yescharacteristic
608Q8—24no—
609Q8—42no—
610Q8—148no—
611Q8—562no—
612Q8—562no—
613Q8—562no—
614D4—24no—
615D4—28no—
616D4—22no—
617D4—24no—
618D4—48no—
619D4—42no—
620D4—48no—
621D4—84no—
622D4#654814yes—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—48no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—84no—
638C2×C4—144no—
639C2×C4—144no—
640C2×C4—562no—
641C2×C4—562no—
642C2×C4—562no—
643C2×C4—562no—
644C2×C4C22×C22⋊D712yes—
645C2×C4C22×C22⋊D711yescharacteristic
646C2×C4C22×C22⋊D712yes—
647C2×C4C22×C22⋊D712yes—
648C2×C4C22×C22⋊D712yes—
649C2×C4C24×D711yescharacteristic
650C8—148no—
651C7#6157011yescharacteristic, complemented, Sylow
652C22—21no—
653C22—22no—
654C22—21no—
655C22—22no—
656C22—22no—
657C22—24no—
658C22—22no—
659C22—22no—
660C22—44no—
661C22—48no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—82no—
668C22—816no—
669C22—84no—
670C22C2×#651412yes—
671C22C2×#651414yes—
672C22C23×C22⋊D711yescharacteristic
673C4—22no—
674C4—21no—
675C4—22no—
676C4—22no—
677C4—22no—
678C4—42no—
679C4—42no—
680C4—284no—
681C4—284no—
682C4C2×#654812yes—
683C2—22no—
684C2—24no—
685C2—42no—
686C2—44no—
687C2—82no—
688C2#1174430711yescharacteristic
689C2C22×#651411yescharacteristic
690C2#1174434511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#546C2
socleC22×C7C23×D4
hypercenterC2×#546D7
hypocenterC7#61570
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11742834C2semidirect
3. #11741529C2semidirect
4. C2×#89990C2semidirect
5. #11740951C2semidirect
6. #11740943C2semidirect
7. #11740394C2semidirect
8. #11740186C2semidirect
9. #11740076C2semidirect
10. #11739760C2semidirect
11. #11739747C2semidirect
25. C2×#6514C22semidirect
27. C22×#1142C22semidirect
29. C2×#6487C22semidirect
30. #90234C22semidirect
32. D4×Dic14C22semidirect
36. #90161C22semidirect
37. #90011C22semidirect
38. #90004C22semidirect
39. #90000C22semidirect
42. #89990C22semidirect
43. C2×#6406C22semidirect
44. #89979C22semidirect
46. #89832C22semidirect
47. #89827C22semidirect
48. #89826C22semidirect
49. #89823C22semidirect
50. #89822C22semidirect
51. #89816C22semidirect
52. #89814C22semidirect
53. #89812C22semidirect
54. #89805C22semidirect
55. #89791C22semidirect
56. #89790C22semidirect
57. #89783C22semidirect
58. #89779C22semidirect
59. #89742C22semidirect
60. #89698C22semidirect
81. C22×Dic14C23semidirect
110. C2×#1144C23semidirect
118. C2×C4⋊Dic7C23semidirect
126. #6487C23semidirect
129. C2×#1136C23semidirect
138. #6432C23semidirect
139. #6432C23semidirect
141. C4×Dic14C23semidirect
142. #6409C23semidirect
147. C22⋊(C7⋊C8)C23semidirect
148. #6384C23semidirect
149. #6381C23semidirect
150. C4⋊(C7⋊C8)C23semidirect
151. #6377C23semidirect
320. C23×C7#137semidirect
604. C23#6514semidirect
651. C7#61570semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#5462
#117428342
#117415292
C2×#899902
#117409512
#117409432
#117403942
#117401862
#117400762
#117397602
#117397472
#615707