Finite Group Databasebeta

← C2×#11737203 #14233594

Subgroups — C2×#11737203 #14233594

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90260C211yesmaximal, characteristic, complemented
2C2×#90233C211yesmaximal, characteristic
3C2×C7×#440C211yesmaximal, characteristic
4C2×#89938C211yesmaximal, characteristic
5C2×#89938C211yesmaximal, characteristic
6C2×#89803C211yesmaximal, characteristic, complemented
7C2×#89781C211yesmaximal, characteristic
8#11737203C2116yesmaximal, direct product factor
9C2×#89649C211yesmaximal, characteristic, complemented
10C2×#89647C211yesmaximal, characteristic, complemented
11C2×#89561C211yesmaximal, characteristic, complemented
12C2×#89562C211yesmaximal, characteristic, complemented
13C2×#89537C211yesmaximal, characteristic
14C2×#89540C211yesmaximal, characteristic
15C2×#89475C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C22×#1144C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C2×#6499C2211yescharacteristic
25C2×#6499C2211yescharacteristic
26C2×#6489—21no—
27C2×#6487—21no—
28#90260—24no—
29#90260C2218yescomplemented
30#90233—24no—
31#90233C2218yes—
32C2×#6453—21no—
33C2×#6453C2211yescharacteristic
34C2×#6451—21no—
35C2×#6451C2211yescharacteristic
36C2×#6450C2211yescharacteristic
37C2×#6450C2211yescharacteristic
38C2×#6442—21no—
39C2×#6442—21no—
40C2×#6433—21no—
41C2×#6433C2211yescharacteristic
42C2×#6432C2211yescharacteristic
43C2×C4×Dic14—21no—
44C2×C4×Dic14C2211yescharacteristic
45C7×#440C2218yes—
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89938C2218yes—
53#89938C2218yes—
54C2×#6390C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89803C2218yescomplemented
63#89781C2218yes—
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89649C2218yescomplemented
70#89647C2218yescomplemented
71#89562C2218yescomplemented
72#89561C2218yescomplemented
73#89540C2218yes—
74#89537C2218yes—
75#89475C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3377—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×Dic14—21no—
82C22×Dic14D411yescharacteristic
83C22×Dic14C2311yescharacteristic
84C22×Dic14C2311yescharacteristic
85C2×C7×SD16—24no—
86C2×C7×SD16C2314yes—
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C4×C7×Q8—22no—
90C4×C7×Q8C2314yes—
91C4×C7×D4—22no—
92C4×C7×D4C2314yes—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4C2311yescharacteristic
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C22⋊C4—21no—
97C2×C42×C7—21no—
98C2×C42×C7C2311yescharacteristic
99C2×C22⋊Dic7—21no—
100C2×C22⋊Dic7—21no—
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103Q8×Dic7—22no—
104Q8×Dic7—22no—
105Q8×Dic7C2314yes—
106Q8×Dic7C2314yes—
107C2×#1144—24no—
108C2×#1144—24no—
109C2×#1144C2314yes—
110C2×#1144C2314yes—
111#6499—22no—
112#6499—22no—
113#6499C2314yes—
114#6499C2314yes—
115#6489—28no—
116C2×C4⋊Dic7—21no—
117C2×C4⋊Dic7—21no—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7D411yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124#6487—28no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4D411yescharacteristic
132C2×Dic7⋊C4D411yescharacteristic
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7C2311yescharacteristic
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141#6453—28no—
142#6453—22no—
143#6453C2314yes—
144#6451—28no—
145#6451—22no—
146#6451C2314yes—
147#6450—22no—
148#6450—22no—
149#6450C2314yes—
150#6450C2314yes—
151#6442—28no—
152#6442—28no—
153#6433—22no—
154#6433—28no—
155#6433C2314yes—
156#6432—22no—
157#6432C2314yes—
158C4×Dic14—28no—
159C4×Dic14D414yes—
160C4×Dic14C2314yes—
161C7×#107C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164C7×#97C2314yes—
165#6406C2314yes—
166#6406C2314yes—
167#6390C2314yes—
168#6390C2314yes—
169#6390C2314yes—
170#6390C2314yes—
171#6389C2314yes—
172Dic7⋊C8C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6384C2314yes—
176#6384C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C2×#557—71no—
181C2×#556—71no—
182#3377—716no—
183C2×#491—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#478—71no—
189C2×#464—71no—
190C2×#464—71no—
191C2×#462—71no—
192C2×#446—71no—
193C2×#441—71no—
194C2×#440D711yescharacteristic
195C2×C4×Q16—71no—
196C24×C7—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—22no—
199C2×C7×Q8#4114yes—
200C2×C7×Q8C2412yes—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—24no—
209C22×C4×C7—44no—
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2411yescharacteristic
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7C2×D411yescharacteristic
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C2×Dic14—22no—
222C2×Dic14—22no—
223C2×Dic14—22no—
224C2×Dic14—22no—
225C2×Dic14—21no—
226C2×Dic14—21no—
227C2×Dic14—24no—
228C2×Dic14—42no—
229C2×Dic14—44no—
230C2×Dic14C2×D414yes—
231C2×Dic14C2412yes—
232C2×Dic14C2412yes—
233C7×SD16—28no—
234C2×C7×C8—22no—
235C2×C7×C8—22no—
236C2×C7×C8C2412yes—
237C2×C7×C8C2412yes—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4C2412yes—
242C7×C4⋊C4C2412yes—
243C7×C22⋊C4—24no—
244C42×C7—24no—
245C42×C7C2×D412yes—
246C42×C7C2412yes—
247C22⋊Dic7—24no—
248C22⋊Dic7—24no—
249C22⋊Dic7—24no—
250C22⋊Dic7—24no—
251#1144—28no—
252#1144—28no—
253C4⋊Dic7—24no—
254C4⋊Dic7—24no—
255C4⋊Dic7—21no—
256C4⋊Dic7—21no—
257C4⋊Dic7—24no—
258C4⋊Dic7—24no—
259C4⋊Dic7—24no—
260C4⋊Dic7C2×D414yes—
261C4⋊Dic7C2412yes—
262C4⋊Dic7C2412yes—
263Dic7⋊C4—24no—
264Dic7⋊C4—24no—
265Dic7⋊C4—24no—
266Dic7⋊C4—24no—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269Dic7⋊C4C2×D414yes—
270Dic7⋊C4C2×D414yes—
271C4×Dic7—24no—
272C4×Dic7—24no—
273C4×Dic7—24no—
274C4×Dic7—24no—
275C4×Dic7C2×D412yes—
276C4×Dic7C2×D412yes—
277C4×Dic7C2412yes—
278C4×Dic7C2412yes—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283C22×Q16—71no—
284C22×Q16—71no—
285C22×SD16C2×D711yescharacteristic
286#557—78no—
287#557—144no—
288#556—78no—
289#556—144no—
290C2×C4⋊Q8—71no—
291C2×C4⋊Q8—71no—
292C2×C4⋊Q8—141no—
293C2×#126—141no—
294C2×#126—141no—
295C2×#125—71no—
296C2×#125—71no—
297C2×#125—141no—
298C2×#125—141no—
299C2×#124—71no—
300C2×#124—71no—
301C2×C22⋊Q8—141no—
302C2×C4×Q8—71no—
303C2×C4×Q8—71no—
304C2×C4×Q8—71no—
305C2×C4×Q8—71no—
306C2×C4×Q8—71no—
307C2×C4×Q8—141no—
308C2×C4×Q8C2×D711yescharacteristic
309C2×C4×D4C2×D711yescharacteristic
310C2×#117—141no—
311#491—78no—
312#489—78no—
313#488—78no—
314#479—78no—
315#478—78no—
316#477—78no—
317#464—78no—
318#464—78no—
319#462—78no—
320#446—78no—
321#441—78no—
322#440C2×D718yes—
323C4×Q16—78no—
324C2×#107—71no—
325C2×#107C2×D711yescharacteristic
326C2×#106—71no—
327C2×C4⋊C8—71no—
328C2×C4⋊C8—71no—
329C2×C4⋊C8—71no—
330C2×#103—71no—
331C2×#103—71no—
332C2×#103—71no—
333C2×#103—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103C2×D711yescharacteristic
337C2×#102—71no—
338C2×#102—71no—
339C2×#102C2×D711yescharacteristic
340C2×#97—71no—
341C2×#97C2×D711yescharacteristic
342C2×C4×C8—71no—
343C23×C7—22no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7C22×D411yescharacteristic
348C7×Q8—24no—
349C7×Q8—22no—
350C7×Q8C2×#4114yes—
351C7×D4—22no—
352C7×D4—22no—
353C7×D4—42no—
354C2×C4×C7—24no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—48no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7C22×D412yes—
364C2×C4×C7C22×D412yes—
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C2×#4112yes—
367C2×C4×C72−1+412yes—
368C2×C4×C7C2511yescharacteristic
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7C22×D412yes—
382C2×Dic7C22×D412yes—
383C2×Dic7C22×D412yes—
384C2×Dic7C22×D412yes—
385Dic14—22no—
386Dic14—22no—
387Dic14—22no—
388Dic14—22no—
389Dic14—44no—
390Dic14—48no—
391Dic14—42no—
392Dic14—42no—
393C7×C8—22no—
394C7×C8—22no—
395C7⋊C8—22no—
396C7⋊C8—22no—
397C22×Q8—71no—
398C22×Q8—71no—
399C22×Q8—71no—
400C22×Q8—141no—
401C22×Q8C22×D711yescharacteristic
402C22×D4C22×D711yescharacteristic
403C23×C4—21no—
404C2×Q16—74no—
405C2×Q16—74no—
406C2×Q16—144no—
407C2×Q16—144no—
408C2×SD16—24no—
409C2×SD16C22×D714yes—
410C22×C8—71no—
411C22×C8—71no—
412C22×C8C22×D711yescharacteristic
413C22×C8C22×D711yescharacteristic
414C4⋊Q8—74no—
415C4⋊Q8—74no—
416C4⋊Q8—142no—
417C4⋊Q8—148no—
418C4⋊Q8—142no—
419#126—148no—
420#126—148no—
421#125—74no—
422#125—74no—
423#125—148no—
424#125—142no—
425#125—148no—
426#125—142no—
427#124—74no—
428#124—74no—
429#124—142no—
430#124—142no—
431C22⋊Q8—148no—
432C4×Q8—22no—
433C4×Q8—74no—
434C4×Q8—74no—
435C4×Q8—74no—
436C4×Q8—74no—
437C4×Q8—74no—
438C4×Q8—74no—
439C4×Q8—148no—
440C4×Q8—142no—
441C4×Q8—142no—
442C4×Q8—142no—
443C4×Q8—142no—
444C4×Q8C22×D714yes—
445C4×D4—22no—
446C4×D4C22×D714yes—
447#117—148no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—71no—
450C2×C4⋊C4—71no—
451C2×C4⋊C4—71no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—141no—
455C2×C4⋊C4—141no—
456C2×C4⋊C4—141no—
457C2×C4⋊C4—141no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4C22×D711yescharacteristic
466C2×C4⋊C4C22×D711yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—141no—
469C2×C22⋊C4—141no—
470C2×C22⋊C4—141no—
471C2×C22⋊C4—141no—
472C2×C42—21no—
473C2×C42—71no—
474C2×C42—71no—
475C2×C42—141no—
476C2×C42—141no—
477C2×C42—141no—
478C2×C42—141no—
479C2×C42C22×D711yescharacteristic
480#107—74no—
481#107C22×D714yes—
482#106—74no—
483C4⋊C8—74no—
484C4⋊C8—74no—
485C4⋊C8—74no—
486#103—74no—
487#103—74no—
488#103—74no—
489#103—74no—
490#103—74no—
491#103—74no—
492#103C22×D714yes—
493#102—74no—
494#102—74no—
495#102C22×D714yes—
496#97—74no—
497#97C22×D714yes—
498C4×C8—74no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—84no—
503C22×C7#54812yes—
504C22×C7#57512yes—
505C22×C7#57812yes—
506C22×C7C23×D411yescharacteristic
507C4×C7—24no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7#54812yes—
513C4×C7C22×#4111yescharacteristic
514C4×C7C2×2−1+411yescharacteristic
515Dic7—22no—
516Dic7—22no—
517Dic7—22no—
518Dic7—22no—
519Dic7—42no—
520Dic7—42no—
521Dic7—42no—
522Dic7—42no—
523C24—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—74no—
527C2×Q8—72no—
528C2×Q8—72no—
529C2×Q8—144no—
530C2×Q8—141no—
531C2×Q8—141no—
532C2×Q8—142no—
533C2×Q8—142no—
534C2×Q8—142no—
535C2×Q8—142no—
536C2×Q8—282no—
537C2×Q8—284no—
538C2×Q8#115714yes—
539C2×Q8C23×D712yes—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4C23×D712yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—44no—
549C22×C4—71no—
550C22×C4—71no—
551C22×C4—71no—
552C22×C4—71no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4D4×D711yescharacteristic
558C22×C4D4×D711yescharacteristic
559C22×C4C23×D711yescharacteristic
560Q16—148no—
561Q16—148no—
562SD16—28no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—72no—
566C2×C8—72no—
567C2×C8—142no—
568C2×C8—142no—
569C2×C8C23×D712yes—
570C2×C8C23×D712yes—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—74no—
575C4⋊C4—74no—
576C4⋊C4—74no—
577C4⋊C4—72no—
578C4⋊C4—72no—
579C4⋊C4—144no—
580C4⋊C4—144no—
581C4⋊C4—144no—
582C4⋊C4—144no—
583C4⋊C4—144no—
584C4⋊C4—144no—
585C4⋊C4—144no—
586C4⋊C4—144no—
587C4⋊C4—144no—
588C4⋊C4—141no—
589C4⋊C4—141no—
590C4⋊C4—144no—
591C4⋊C4—144no—
592C4⋊C4C23×D712yes—
593C4⋊C4C23×D712yes—
594C22⋊C4—24no—
595C22⋊C4—144no—
596C22⋊C4—144no—
597C22⋊C4—144no—
598C22⋊C4—144no—
599C42—24no—
600C42—72no—
601C42—72no—
602C42—72no—
603C42—72no—
604C42—144no—
605C42—144no—
606C42—144no—
607C42—144no—
608C42D4×D712yes—
609C42C23×D712yes—
610C2×C7—82no—
611C2×C7#337714yescomplemented
612C2×C7C2×#54811yescharacteristic
613C2×C7C2×#57511yescharacteristic
614C2×C7C2×#57811yescharacteristic
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C2×D4×D711yescharacteristic
620Q8—24no—
621Q8—22no—
622Q8—142no—
623Q8—142no—
624Q8—142no—
625Q8—142no—
626Q8—284no—
627Q8—288no—
628Q8—282no—
629Q8—282no—
630Q8C2×#115714yes—
631D4—22no—
632D4—22no—
633D4—42no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—72no—
644C2×C4—72no—
645C2×C4—72no—
646C2×C4—72no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—282no—
656C2×C4—282no—
657C2×C4—282no—
658C2×C4—282no—
659C2×C4C2×#115712yes—
660C2×C4C2×D4×D712yes—
661C2×C4C2×D4×D712yes—
662C2×C4C2×D4×D711yescharacteristic
663C2×C4#655412yes—
664C2×C4C24×D711yescharacteristic
665C8—22no—
666C8—22no—
667C8—142no—
668C8—142no—
669C7C2×#337711yescharacteristic, complemented, Sylow
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#9024312yes—
675C22#9046412yes—
676C22#9047012yes—
677C22C22×D4×D711yescharacteristic
678C4—22no—
679C4—22no—
680C4—24no—
681C4—42no—
682C4—42no—
683C4—142no—
684C4—142no—
685C4—142no—
686C4—142no—
687C4—282no—
688C4—282no—
689C4—282no—
690C4—282no—
691C4#9024312yes—
692C4C22×#115711yescharacteristic
693C4C2×#655411yescharacteristic
694C2—82no—
695C2#1173720314yesdirect product factor
696C2C2×#9024311yescharacteristic
697C2C2×#9046411yescharacteristic
698C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×#440D7
hypocenterC7C2×#3377
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90260C2semidirect
6. C2×#89803C2semidirect
8. #11737203C2direct (N × H)
9. C2×#89649C2semidirect
10. C2×#89647C2semidirect
11. C2×#89561C2semidirect
12. C2×#89562C2semidirect
15. C2×#89475C2semidirect
16. C2×#89473C2semidirect
29. #90260C22semidirect
62. #89803C22semidirect
69. #89649C22semidirect
70. #89647C22semidirect
71. #89562C22semidirect
72. #89561C22semidirect
75. #89475C22semidirect
76. #89473C22semidirect
611. C2×C7#3377semidirect
669. C7C2×#3377semidirect
695. C2#11737203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902602
C2×#902332
C2×C7×#4402
C2×#899382
C2×#898032
C2×#897812
#117372032
C2×#896492
C2×#896472
C2×#895612
C2×#895622
C2×#895372
C2×#895402
C2×#894752
C2×#894732
C2×#33777