Subgroups — #73318

Order 384.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#874	C₂	1	14	yes	maximal, complemented
2	C₃×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
3	#2867	—	3	1	no	maximal, Sylow
4	C₂²×D₁₂	C₂²	1	28	yes	—
5	C₂×C₃×C₄²	C₂²	1	7	yes	—
6	#874	—	2	56	no	—
7	C₂×#127	—	3	14	no	—
8	C₄³	D₃	1	1	yes	characteristic, complemented
9	C₂³×D₃	C₂³	1	8	yes	—
10	C₂²×C₃×C₄	C₂³	1	7	yes	—
11	C₂×D₁₂	—	2	168	no	—
12	C₃×C₄²	D₄	1	28	yes	complemented
13	C₂²×D₄	—	3	28	no	—
14	#127	—	6	56	no	—
15	C₂×C₄²	C₂×D₃	1	7	yes	—
16	C₂³×C₃	C₂⁴	1	1	yes	characteristic
17	C₂²×D₃	—	2	56	no	—
18	C₂×C₃×C₄	C₂×D₄	1	42	yes	—
19	D₁₂	—	4	112	no	—
20	C₂⁴	—	3	8	no	—
21	C₂×D₄	—	6	168	no	—
22	C₂²×C₄	C₂²×D₃	1	7	yes	—
23	C₄²	D₁₂	1	28	yes	complemented
24	C₂²×C₃	C₂²×D₄	1	7	yes	—
25	C₂×D₃	—	4	56	no	—
26	C₃×C₄	#127	1	28	yes	complemented
27	C₂³	—	6	56	no	—
28	C₂³	C₂³×D₃	1	1	yes	characteristic
29	D₄	—	12	112	no	—
30	C₂×C₄	C₂×D₁₂	1	42	yes	—
31	C₂×C₃	C₂×#127	1	7	yes	—
32	D₃	—	8	8	no	—
33	C₂²	—	12	56	no	—
34	C₂²	C₂²×D₁₂	1	7	yes	—
35	C₄	#874	1	28	yes	complemented
36	C₃	#2867	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	24	8	no	—
38	C₂	C₂×#874	1	7	yes	—

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.