Subgroups — #401×D₆₇ #22563504

Order 8576.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇⋊#401	C₂	1	7	yes	maximal, complemented
2	#95×D₆₇	C₂	1	7	yes	maximal
3	#401×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₆₇	C₂²	1	7	yes	—
5	C₆₇⋊#95	C₂²	1	21	yes	—
6	#95×C₆₇	C₂²	1	7	yes	—
7	C₂³×D₆₇	C₂³	1	1	yes	characteristic
8	C₂²×Dic₆₇	C₂³	1	7	yes	—
9	C₂×C₄×D₆₇	—	2	42	no	—
10	C₂²×C₄×C₆₇	C₂³	1	7	yes	—
11	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
12	C₂²×D₆₇	#41	1	14	yes	—
13	C₂×C₄×C₆₇	—	2	21	no	—
14	C₂×Dic₆₇	—	2	21	no	—
15	C₄×D₆₇	—	4	28	no	—
16	C₂²×C₆₇	C₂×#41	1	7	yes	—
17	C₂×D₆₇	#126	1	28	yes	—
18	C₄×C₆₇	—	4	7	no	—
19	Dic₆₇	—	4	7	no	—
20	C₂×C₆₇	C₂×#126	1	7	yes	—
21	D₆₇	#401	1	8	yes	direct product factor
22	C₂×#401	—	67	1	no	maximal, Sylow
23	C₆₇	C₂×#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	67	7	no	—
25	#401	D₆₇	1	1	yes	characteristic, direct product factor
26	C₂×#95	—	67	7	no	—
27	C₂³×C₄	—	67	7	no	—
28	#95	—	67	21	no	—
29	#95	C₂×D₆₇	1	7	yes	—
30	C₂⁴	—	67	1	no	—
31	C₂²×C₄	—	67	7	no	—
32	C₂²×C₄	—	134	42	no	—
33	C₂²×C₄	C₂²×D₆₇	1	7	yes	—
34	C₂³	—	67	14	no	—
35	C₂³	C₂³×D₆₇	1	1	yes	characteristic
36	C₂×C₄	—	2	21	no	—
37	C₂×C₄	—	268	28	no	—
38	C₂×C₄	—	134	21	no	—
39	C₂²	—	67	28	no	—
40	C₂²	#41×D₆₇	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	268	7	no	—
43	C₂	—	67	8	no	—
44	C₂	#126×D₆₇	1	7	yes	—

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