Subgroups — #21418604

Order 7456.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11745400	C₂	1	2	yes	maximal
2	C₈×D₂₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745400	—	2	2	no	—
4	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
5	#14272338	C₄	1	1	yes	characteristic, complemented
6	C₈×C₂₃₃	C₄	1	1	yes	characteristic, complemented
7	C₂×D₂₃₃	D₄	1	1	yes	characteristic
8	#11745400	—	4	2	no	—
9	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
10	Dic₂₃₃	Q₈	1	1	yes	characteristic
11	C₂×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
12	D₂₃₃	D₈	1	1	yes	characteristic
13	D₂₃₃	Q₁₆	1	1	yes	characteristic
14	C₂₃₃	#107	1	1	yes	characteristic, complemented, Sylow
15	#107	—	233	1	no	maximal, Sylow
16	C₂×C₈	—	233	1	no	—
17	C₄⋊C₄	—	233	2	no	—
18	C₂×C₄	—	466	2	no	—
19	C₂×C₄	—	233	1	no	—
20	C₈	—	233	1	no	—
21	C₈	#11745400	1	1	yes	characteristic, complemented
22	C₂²	—	233	1	no	—
23	C₄	—	932	2	no	—
24	C₄	—	233	1	no	—
25	C₄	C₂×#11745400	1	1	yes	characteristic
26	C₂	—	233	1	no	—
27	C₂	—	233	1	no	—
28	C₂	C₄⋊#11745400	1	1	yes	characteristic

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