Subgroups — #17989511

Order 4672.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556661	C₂	1	1	yes	maximal, characteristic
2	#14556659	C₂	1	1	yes	maximal, characteristic
3	#14556530	C₂	1	1	yes	maximal, characteristic
4	#11924038	—	2	1	no	—
5	C₄⋊#64408	—	2	1	no	—
6	C₈×D₇₃	C₂²	1	1	yes	characteristic
7	#11924003	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
9	C₂×#64408	—	4	1	no	—
10	C₄×D₇₃	D₄	1	1	yes	characteristic
11	#10596833	—	4	1	no	—
12	C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
13	#10596831	Q₈	1	1	yes	characteristic
14	C₂×D₇₃	SD₁₆	1	1	yes	characteristic
15	#64408	—	8	1	no	—
16	C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	Dic₇₃	SD₁₆	1	1	yes	characteristic
18	C₂×C₇₃	#106	1	1	yes	characteristic
19	D₇₃	—	2	1	no	—
20	C₇₃	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	73	1	no	maximal, Sylow
22	M₃₂	—	73	1	no	—
23	#108	—	73	1	no	—
24	#106	—	73	1	no	—
25	M₁₆	—	146	1	no	—
26	C₂×C₈	—	73	1	no	—
27	C₄⋊C₄	—	146	1	no	—
28	C₁₆	—	73	1	no	—
29	C₁₆	#64408	1	1	yes	characteristic, complemented
30	C₂×C₄	—	292	1	no	—
31	C₂×C₄	—	73	1	no	—
32	C₈	—	292	1	no	—
33	C₈	—	73	1	no	—
34	C₈	C₂×#64408	1	1	yes	characteristic
35	C₂²	—	73	1	no	—
36	C₄	—	584	1	no	—
37	C₄	—	73	1	no	—
38	C₄	C₄⋊#64408	1	1	yes	characteristic
39	C₂	—	146	1	no	—
40	C₂	#14556659	1	1	yes	characteristic

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

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