Subgroups — #22558424

Order 8576.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₀₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic
4	Dic₅₃₆	—	2	1	no	—
5	D₁₆×C₆₇	—	2	1	no	—
6	C₃₂×C₆₇	C₂²	1	1	yes	characteristic
7	Dic₂₆₈	—	4	1	no	—
8	D₈×C₆₇	—	4	1	no	—
9	C₁₆×C₆₇	D₄	1	1	yes	characteristic
10	D₄×C₆₇	—	8	1	no	—
11	Dic₁₃₄	—	8	1	no	—
12	C₈×C₆₇	D₈	1	1	yes	characteristic
13	C₂²×C₆₇	—	16	1	no	—
14	C₄×C₆₇	D₁₆	1	1	yes	characteristic
15	Dic₆₇	—	16	1	no	—
16	C₂×C₆₇	—	32	1	no	—
17	C₂×C₆₇	D₃₂	1	1	yes	characteristic
18	SD₁₂₈	—	67	1	no	maximal, Sylow
19	C₆₇	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	67	1	no	—
21	D₃₂	D₆₇	1	1	yes	characteristic
22	C₆₄	—	67	1	no	—
23	Q₃₂	—	134	1	no	—
24	D₁₆	—	2	1	no	—
25	C₃₂	C₂×D₆₇	1	1	yes	characteristic
26	Q₁₆	—	268	1	no	—
27	D₈	—	4	1	no	—
28	C₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
29	Q₈	—	536	1	no	—
30	D₄	—	8	1	no	—
31	C₈	#11761613	1	1	yes	characteristic
32	C₂²	—	16	1	no	—
33	C₄	—	1072	1	no	—
34	C₄	#14523984	1	1	yes	characteristic
35	C₂	—	32	1	no	—
36	C₂	#16863231	1	1	yes	characteristic

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