Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
425 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 425 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10592537 | C2 | semidirect |
| 2. #10590375 | C2 | semidirect |
| 4. #10590313 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 6. C3×#4482 | C2 | semidirect |
| 7. #10589100 | C2 | semidirect |
| 36. #4485 | D3 | semidirect |
| 37. #4482 | D3 | semidirect |
| 116. C3⋊(C3⋊C8) | D8 | semidirect |
| 325. C32 | #1685 | semidirect |
| 378. C3 | #68398 | semidirect |
| 379. C3 | #68448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592537 | 2 |
| #10590375 | 2 |
| #10590355 | 2 |
| #10590313 | 2 |
| C3×#4485 | 2 |
| C3×#4482 | 2 |
| #10589100 | 2 |
| #68448 | 3 |
| #68398 | 3 |