Subgroups — #28417493

Order 14912.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418609	C₂	1	3	yes	maximal, complemented
2	C₂×#16836597	C₂	1	3	yes	maximal, complemented
3	#21418542	C₂	1	1	yes	maximal, characteristic
4	#16836597	C₂²	1	1	yes	characteristic
5	#16836597	C₂²	1	3	yes	—
6	#16836578	C₄	1	3	yes	—
7	C₂×#14272338	C₂²	1	3	yes	—
8	#41×C₂₃₃	C₄	1	1	yes	characteristic
9	#14272338	C₂×C₄	1	3	yes	—
10	#14272338	C₂³	1	1	yes	characteristic
11	Q₈×C₂₃₃	C₈	1	1	yes	characteristic
12	D₄×C₂₃₃	C₈	1	3	yes	—
13	C₂×C₄×C₂₃₃	C₂×C₄	1	3	yes	—
14	C₂²×C₂₃₃	C₂×C₈	1	3	yes	—
15	C₄×C₂₃₃	C₂×C₈	1	3	yes	—
16	C₄×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₂₃₃	—	2	3	no	—
18	C₂×C₂₃₃	C₂²×C₈	1	1	yes	characteristic
19	C₂₃₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	233	1	no	maximal, Sylow
21	#131	—	233	1	no	—
22	M₃₂	—	233	3	no	—
23	C₂×C₁₆	—	233	3	no	—
24	#41	#11745400	1	1	yes	characteristic
25	M₁₆	—	233	3	no	—
26	C₂×C₈	—	233	3	no	—
27	C₁₆	—	233	1	no	—
28	C₁₆	—	233	3	no	—
29	Q₈	#14272345	1	1	yes	characteristic
30	D₄	#14272345	1	3	yes	—
31	C₂×C₄	C₂×#11745400	1	3	yes	—
32	C₈	—	233	1	no	—
33	C₈	—	233	3	no	—
34	C₂²	C₂×#14272345	1	3	yes	—
35	C₄	C₂×#14272345	1	3	yes	—
36	C₄	C₂²×#11745400	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#14272345	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.