Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C8×Q8 | C2 | semidirect |
| 4. #10589401 | C2 | semidirect |
| 6. #10589346 | C2 | semidirect |
| 7. #10589321 | C2 | semidirect |
| 24. C3×C8×Q8 | D3 | semidirect |
| 67. C32×Q8 | M16 | semidirect |
| 80. C32×C8 | SD16 | semidirect |
| 85. C8×Q8 | C3⋊D3 | semidirect |
| 139. C3×Q8 | ΓL(1,𝔽25) | semidirect |
| 152. C3×C8 | #215 | semidirect |
| 191. C32 | #1583 | semidirect |
| 194. Q8 | #3743 | semidirect |
| 211. C8 | #3755 | semidirect |
| 228. C3 | #70933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| C4×#3755 | 2 |
| #10592387 | 2 |
| #10589401 | 2 |
| #10589349 | 2 |
| #10589346 | 2 |
| #10589321 | 2 |
| #70933 | 3 |