Subgroups — #27131328

Order 12128.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₁₆	C₂	1	6	yes	maximal, complemented
2	C₄²×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₃₇₉	C₂²	1	4	yes	—
4	D₁₅₁₆	—	2	12	no	—
5	C₂×C₄×C₃₇₉	C₂²	1	3	yes	—
6	C₂²×C₃₇₉	C₂³	1	1	yes	characteristic
7	C₂×D₃₇₉	—	2	12	no	—
8	C₄×C₃₇₉	D₄	1	6	yes	complemented
9	C₂×C₃₇₉	C₂×D₄	1	3	yes	—
10	D₃₇₉	—	4	4	no	—
11	C₃₇₉	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	379	1	no	maximal, Sylow
13	C₂×D₄	—	379	6	no	—
14	C₄²	D₃₇₉	1	1	yes	characteristic, complemented
15	C₂³	—	379	4	no	—
16	D₄	—	758	12	no	—
17	C₂×C₄	C₂×D₃₇₉	1	3	yes	—
18	C₂²	—	758	12	no	—
19	C₂²	C₂²×D₃₇₉	1	1	yes	characteristic
20	C₄	D₁₅₁₆	1	6	yes	complemented
21	C₂	—	1516	4	no	—
22	C₂	C₂×D₁₅₁₆	1	3	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.