Subgroups — #21418445

Order 7456.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14272338	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃₃	C₄	1	2	yes	—
5	#14272338	C₄	1	2	yes	complemented
6	C₂×C₄×C₂₃₃	C₂²	1	1	yes	characteristic
7	C₈×C₂₃₃	C₄	1	2	yes	complemented
8	C₂²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
10	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
11	Dic₂₃₃	—	2	2	no	—
12	C₂×C₂₃₃	C₄²	1	1	yes	characteristic
13	C₂×C₂₃₃	M₁₆	1	2	yes	—
14	C₂₃₃	#97	1	1	yes	characteristic, complemented, Sylow
15	#97	—	233	1	no	maximal, Sylow
16	C₂×C₈	—	233	1	no	—
17	C₂×C₈	D₂₃₃	1	1	yes	characteristic
18	C₄²	—	233	1	no	—
19	C₂×C₄	—	233	2	no	—
20	C₂×C₄	C₂×D₂₃₃	1	1	yes	characteristic
21	C₈	—	233	2	no	—
22	C₈	Dic₂₃₃	1	2	yes	complemented
23	C₂²	C₄×D₂₃₃	1	1	yes	characteristic
24	C₄	—	466	2	no	—
25	C₄	C₄×D₂₃₃	1	1	yes	characteristic
26	C₄	C₂×Dic₂₃₃	1	1	yes	characteristic
27	C₂	C₄×Dic₂₃₃	1	1	yes	characteristic
28	C₂	#16836577	1	2	yes	—

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