Finite Group Databasebeta

← C7×#16601 #13193817

Subgroups — C7×#16601 #13193817

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×C7×#400C211yesmaximal, characteristic, complemented
3C2×C7×#395C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic
5C7×#1446C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1444C212yesmaximal, complemented
8C7×#1442C212yesmaximal, complemented
9C7×#1440C212yesmaximal
10C7×#1439C212yesmaximal
11C7×C22⋊#95C211yesmaximal, characteristic
12C23×C7×Q8C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×C22⋊Q8—24no—
15C2×C7×C22⋊Q8—24no—
16C2×C7×C22⋊Q8—24no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C7×#400—24no—
27C7×#395—24no—
28C7×#385—24no—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#16601C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C22×C7×Q8—22no—
44C22×C7×Q8—22no—
45C22×C7×Q8—42no—
46C22×C7×Q8—42no—
47C22×C7×Q8D414yes—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—42no—
51C23×C4×C7—42no—
52C23×C4×C7D414yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2312yes—
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C7×C22⋊Q8—232no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—42no—
75C2×C7×C4⋊C4—42no—
76C2×C7×C4⋊C4—42no—
77C2×C7×C4⋊C4D414yes—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4Q814yescomplemented
89C7×#95—22no—
90C7×#95—22no—
91C7×#95—24no—
92C7×#95—22no—
93C7×#95—24no—
94C7×#95—22no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—42no—
101C22×C22⋊Q8C2×C711yescharacteristic
102C2×#400C2×C711yescharacteristic, complemented
103C2×#395C2×C711yescharacteristic, complemented
104C2×#385C2×C711yescharacteristic
105#1446C2×C711yescharacteristic, complemented
106#1445C2×C711yescharacteristic, complemented
107#1444C2×C712yescomplemented
108#1442C2×C712yescomplemented
109#1440C2×C712yes—
110#1439C2×C712yes—
111C22⋊#95C2×C711yescharacteristic
112C24×C7—21no—
113C24×C7—21no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7C2×D412yes—
121C24×C7C2×Q812yes—
122C24×C7#4112yes—
123C24×C7C2411yescharacteristic
124C2×C7×Q8—28no—
125C2×C7×Q8—48no—
126C2×C7×Q8—44no—
127C2×C7×Q8—44no—
128C2×C7×Q8—48no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—28no—
164C22×C4×C7—22no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—44no—
182C22×C4×C7—44no—
183C22×C4×C7—48no—
184C22×C4×C7—48no—
185C22×C4×C7C2×D414yes—
186C22×C4×C7C2×D414yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×Q812yes—
192C22×C4×C7C2×Q812yes—
193C22×C4×C7#4114yes—
194C7×C4⋊C4—216no—
195C7×C4⋊C4—28no—
196C7×C4⋊C4—44no—
197C7×C4⋊C4—48no—
198C7×C4⋊C4—44no—
199C7×C22⋊C4—216no—
200C7×C22⋊C4—28no—
201C7×C22⋊C4—48no—
202C7×C22⋊C4—44no—
203C23×Q8C22×C711yescharacteristic
204C24×C4C22×C711yescharacteristic
205C2×C22⋊Q8—24no—
206C2×C22⋊Q8—24no—
207C2×C22⋊Q8—24no—
208C22×C4⋊C4C22×C711yescharacteristic
209C22×C4⋊C4C22×C712yes—
210C22×C4⋊C4C22×C711yescharacteristic
211C22×C4⋊C4C22×C712yes—
212C22×C4⋊C4C22×C711yescharacteristic
213C22×C22⋊C4C22×C712yes—
214C22×C22⋊C4C22×C712yes—
215C22×C22⋊C4C22×C711yescharacteristic
216C22×C22⋊C4C22×C711yescharacteristic
217#400—24no—
218#395—24no—
219#385—24no—
220C2×#95C22×C711yescharacteristic
221C2×#95C22×C712yes—
222C2×#95C22×C711yescharacteristic
223C2×#95C22×C712yes—
224C2×#95C22×C712yes—
225C2×#95C22×C712yes—
226C2×#95C22×C712yes—
227C2×#95C22×C711yescharacteristic
228C2×#95C22×C711yescharacteristic
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C23×C7—22no—
233C23×C7—22no—
234C23×C7—22no—
235C23×C7—22no—
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—24no—
239C23×C7—24no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—22no—
244C23×C7—24no—
245C23×C7—24no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—42no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7C22⋊Q814yes—
255C23×C7C22×D411yescharacteristic
256C23×C7C22×D411yescharacteristic
257C23×C7C22×D411yescharacteristic
258C23×C7C22×Q811yescharacteristic
259C23×C7C2×#4111yescharacteristic
260C23×C7C2×#4112yes—
261C23×C7H(5,𝔽2)12yes—
262C23×C7H(5,𝔽2)12yes—
263C23×C72−1+411yescharacteristic
264C23×C72−1+412yes—
265C23×C72−1+411yescharacteristic
266C7×Q8—416no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—24no—
270C2×C4×C7—24no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—24no—
278C2×C4×C7—22no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—24no—
282C2×C4×C7—24no—
283C2×C4×C7—24no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—24no—
287C2×C4×C7—24no—
288C2×C4×C7—416no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—42no—
292C2×C4×C7—41no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7—42no—
299C2×C4×C7—42no—
300C2×C4×C7—41no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7#12014yes—
328C25C23×C711yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8—42no—
333C22×Q8C7×D414yes—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4C7×D414yes—
339C23×C4C23×C711yescharacteristic
340C23×C4C23×C712yes—
341C23×C4C23×C711yescharacteristic
342C23×C4C23×C712yes—
343C23×C4C23×C712yes—
344C23×C4C23×C711yescharacteristic
345C23×C4C23×C711yescharacteristic
346C23×C4C23×C711yescharacteristic
347C23×C4C23×C712yes—
348C23×C4C23×C711yescharacteristic
349C22⋊Q8—232no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4C7×D414yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4C7×Q814yescomplemented
375#95—22no—
376#95—22no—
377#95—24no—
378#95—22no—
379#95—24no—
380#95—22no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—42no—
385#95—42no—
386#95—42no—
387C22×C7—24no—
388C22×C7—24no—
389C22×C7—24no—
390C22×C7—42no—
391C22×C7—42no—
392C22×C7—42no—
393C22×C7—42no—
394C22×C7—44no—
395C22×C7—44no—
396C22×C7—44no—
397C22×C7—44no—
398C22×C7C2×#12011yescharacteristic
399C22×C7C2×C22⋊Q811yescharacteristic
400C22×C7#53211yescharacteristic
401C22×C7#53411yescharacteristic
402C22×C7#53411yescharacteristic
403C22×C7#53412yes—
404C22×C7#53512yes—
405C22×C7#53611yescharacteristic
406C22×C7#53611yescharacteristic
407C22×C7#53912yes—
408C22×C7#53912yes—
409C22×C7#54212yes—
410C22×C7#54412yes—
411C22×C7#54712yes—
412C22×C7#54811yescharacteristic
413C22×C7#54811yescharacteristic
414C22×C7#54812yes—
415C22×C7D4×Q811yescharacteristic
416C22×C7D4×Q811yescharacteristic
417C22×C7#55112yes—
418C22×C7#55412yes—
419C22×C7#56312yes—
420C22×C7#56312yes—
421C4×C7—24no—
422C4×C7—42no—
423C4×C7—42no—
424C4×C7—44no—
425C4×C7—42no—
426C4×C7—44no—
427C4×C7—44no—
428C4×C7—81no—
429C4×C7—81no—
430C4×C7—82no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24C2×C7×D412yes—
440C24C2×C7×Q812yes—
441C24C7×#4112yes—
442C24C24×C711yescharacteristic
443C2×Q8—28no—
444C2×Q8—48no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4C2×C7×D414yes—
505C22×C4C2×C7×D414yes—
506C22×C4C2×C7×D412yes—
507C22×C4C2×C7×D412yes—
508C22×C4C2×C7×D412yes—
509C22×C4C2×C7×D412yes—
510C22×C4C2×C7×Q812yes—
511C22×C4C2×C7×Q812yes—
512C22×C4C7×#4114yes—
513C4⋊C4—216no—
514C4⋊C4—28no—
515C4⋊C4—44no—
516C4⋊C4—48no—
517C4⋊C4—44no—
518C22⋊C4—216no—
519C22⋊C4—28no—
520C22⋊C4—48no—
521C22⋊C4—44no—
522C2×C7—44no—
523C2×C7#240911yescharacteristic
524C2×C7#243211yescharacteristic
525C2×C7#256411yescharacteristic
526C2×C7#261311yescharacteristic
527C2×C7#262711yescharacteristic
528C2×C7#266311yescharacteristic
529C2×C7#272012yes—
530C2×C7#272312yes—
531C2×C7#272812yes—
532C2×C7#272912yes—
533C2×C7#281711yescharacteristic
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—24no—
547C23—24no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23C7×C22⋊Q814yes—
557C23C22×C7×D411yescharacteristic
558C23C22×C7×D411yescharacteristic
559C23C22×C7×D411yescharacteristic
560C23C22×C7×Q811yescharacteristic
561C23C2×C7×#4111yescharacteristic
562C23C2×C7×#4112yes—
563C23C7×H(5,𝔽2)12yes—
564C23C7×H(5,𝔽2)12yes—
565C23C7×2−1+411yescharacteristic
566C23C7×2−1+412yes—
567C23C7×2−1+411yescharacteristic
568Q8—416no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—416no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4C7×#12014yes—
630C7#1660111yescharacteristic, direct product factor, Sylow
631C22—24no—
632C22—24no—
633C22—24no—
634C22—42no—
635C22—42no—
636C22—44no—
637C22—44no—
638C22—44no—
639C22—44no—
640C22—42no—
641C22—42no—
642C22C2×C7×#12011yescharacteristic
643C22C2×C7×C22⋊Q811yescharacteristic
644C22C7×#53211yescharacteristic
645C22C7×#53411yescharacteristic
646C22C7×#53412yes—
647C22C7×#53411yescharacteristic
648C22C7×#53512yes—
649C22C7×#53611yescharacteristic
650C22C7×#53611yescharacteristic
651C22C7×#53912yes—
652C22C7×#53912yes—
653C22C7×#54212yes—
654C22C7×#54412yes—
655C22C7×#54712yes—
656C22C7×#54811yescharacteristic
657C22C7×#54811yescharacteristic
658C22C7×#54812yes—
659C22C7×D4×Q811yescharacteristic
660C22C7×D4×Q811yescharacteristic
661C22C7×#55112yes—
662C22C7×#55412yes—
663C22C7×#56312yes—
664C22C7×#56312yes—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—44no—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—81no—
673C4—82no—
674C4—81no—
675C2—44no—
676C2C7×#240911yescharacteristic
677C2C7×#243211yescharacteristic
678C2C7×#256411yescharacteristic
679C2C7×#261311yescharacteristic
680C2C7×#262711yescharacteristic
681C2C7×#266311yescharacteristic
682C2C7×#272012yes—
683C2C7×#272312yes—
684C2C7×#272812yes—
685C2C7×#272912yes—
686C2C7×#281711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#400C2semidirect
3. C2×C7×#395C2semidirect
5. C7×#1446C2semidirect
6. C7×#1445C2semidirect
7. C7×#1444C2semidirect
8. C7×#1442C2semidirect
41. #16601C7direct (N × H)
88. C2×C7×C22⋊C4Q8semidirect
102. C2×#400C2×C7semidirect
103. C2×#395C2×C7semidirect
105. #1446C2×C7semidirect
106. #1445C2×C7semidirect
107. #1444C2×C7semidirect
108. #1442C2×C7semidirect
374. C2×C22⋊C4C7×Q8semidirect
630. C7#16601direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×C7×#4002
C2×C7×#3952
C2×C7×#3852
C7×#14462
C7×#14452
C7×#14442
C7×#14422
C7×#14402
C7×#14392
C7×C22⋊#952
#166017