Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
406 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10592541 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. #10590273 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 6. C3×#4480 | C2 | semidirect |
| 7. #10589096 | C2 | semidirect |
| 36. #4485 | D3 | semidirect |
| 39. #4480 | D3 | semidirect |
| 315. C32 | #1677 | semidirect |
| 367. C3 | #68396 | semidirect |
| 368. C3 | #68538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592541 | 2 |
| #10590355 | 2 |
| #10590327 | 2 |
| #10590273 | 2 |
| C3×#4485 | 2 |
| C3×#4480 | 2 |
| #10589096 | 2 |
| #68538 | 3 |
| #68396 | 3 |