Subgroups — C₂³×#15667732 #36378857

Order 22592.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667732	C₂	1	14	yes	maximal, direct product factor
2	C₂³×Dic₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667732	C₂²	1	28	yes	direct product factor
4	C₂²×Dic₃₅₃	C₄	1	7	yes	—
5	C₂²×Dic₃₅₃	C₂²	1	7	yes	—
6	C₂⁴×C₃₅₃	C₄	1	1	yes	characteristic
7	#15667732	C₂³	1	8	yes	direct product factor
8	C₂×Dic₃₅₃	C₂×C₄	1	21	yes	—
9	C₂×Dic₃₅₃	C₂³	1	7	yes	—
10	C₂³×C₃₅₃	C₈	1	8	yes	complemented
11	C₂³×C₃₅₃	C₂×C₄	1	7	yes	—
12	C₂²×C₃₅₃	C₂×C₈	1	28	yes	complemented
13	C₂²×C₃₅₃	C₂²×C₄	1	7	yes	—
14	Dic₃₅₃	C₂²×C₄	1	7	yes	—
15	Dic₃₅₃	C₂⁴	1	1	yes	characteristic
16	C₂×C₃₅₃	C₂²×C₈	1	14	yes	complemented
17	C₂×C₃₅₃	C₂³×C₄	1	1	yes	characteristic
18	C₃₅₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	353	1	no	maximal, Sylow
20	C₂³×C₄	—	353	1	no	—
21	C₂²×C₈	—	353	14	no	—
22	C₂⁴	#13083443	1	1	yes	characteristic
23	C₂²×C₄	—	353	7	no	—
24	C₂²×C₄	—	353	7	no	—
25	C₂×C₈	—	353	28	no	—
26	C₂³	#15667732	1	8	yes	direct product factor
27	C₂³	C₂×#13083443	1	7	yes	—
28	C₂×C₄	—	353	21	no	—
29	C₂×C₄	—	353	7	no	—
30	C₈	—	353	8	no	—
31	C₂²	C₂×#15667732	1	28	yes	direct product factor
32	C₂²	C₂²×#13083443	1	7	yes	—
33	C₄	—	353	1	no	—
34	C₄	—	353	7	no	—
35	C₂	C₂²×#15667732	1	14	yes	direct product factor
36	C₂	C₂³×#13083443	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.