Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1338 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1338 conjugacy classes of subgroups — too many to draw. Only its 297 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. #10595948 | C2 | semidirect |
| 2. C32×C4×M16 | C2 | semidirect |
| 3. #10592834 | C2 | semidirect |
| 4. #10592410 | C2 | semidirect |
| 5. #10592394 | C2 | semidirect |
| 6. #10592393 | C2 | semidirect |
| 7. #10592379 | C2 | semidirect |
| 26. C3×C4×M16 | D3 | semidirect |
| 85. C32×C8 | #41 | semidirect |
| 92. C4×M16 | C3⋊D3 | semidirect |
| 156. C3×C8 | #235 | semidirect |
| 192. C32 | #3184 | semidirect |
| 209. C8 | #3828 | semidirect |
| 225. C3 | #78535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×C4×M16 | 2 |
| #10592834 | 2 |
| #10592410 | 2 |
| #10592394 | 2 |
| #10592393 | 2 |
| #10592379 | 2 |
| #78535 | 3 |