Subgroups — #21418598

Order 7456.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16836602	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11745400	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745400	—	2	1	no	—
5	#14272345	—	2	1	no	—
6	Dic₄₆₆	—	2	1	no	—
7	Dic₄₆₆	C₄	1	1	yes	characteristic, complemented
8	C₄×D₂₃₃	—	2	1	no	—
9	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
10	Q₈×C₂₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂×D₂₃₃	D₄	1	1	yes	characteristic
12	#11745400	—	4	1	no	—
13	C₄×C₂₃₃	—	2	1	no	—
14	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
15	Dic₂₃₃	—	2	1	no	—
16	Dic₂₃₃	D₄	1	1	yes	characteristic
17	C₂×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
18	D₂₃₃	SD₁₆	1	1	yes	characteristic
19	D₂₃₃	Q₁₆	1	1	yes	characteristic
20	C₂₃₃	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	233	1	no	maximal, Sylow
22	C₂×Q₈	—	233	1	no	—
23	C₂×C₈	—	233	1	no	—
24	C₄⋊C₄	—	233	1	no	—
25	Q₈	—	466	1	no	—
26	Q₈	—	233	1	no	—
27	Q₈	#11745400	1	1	yes	characteristic, complemented
28	C₂×C₄	—	466	1	no	—
29	C₂×C₄	—	466	1	no	—
30	C₂×C₄	—	233	1	no	—
31	C₈	—	466	1	no	—
32	C₂²	—	233	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	932	1	no	—
35	C₄	—	466	1	no	—
36	C₄	—	233	1	no	—
37	C₄	C₂×#11745400	1	1	yes	characteristic
38	C₂	—	233	1	no	—
39	C₂	—	233	1	no	—
40	C₂	C₂²⋊#11745400	1	1	yes	characteristic

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