Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
308 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 308 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. C3×#4895 | C2 | semidirect |
| 2. #10590915 | C2 | semidirect |
| 4. #10589359 | C2 | semidirect |
| 5. C3×#4497 | C2 | semidirect |
| 6. #10589121 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 21. #63550 | C4 | semidirect |
| 22. #63547 | C4 | semidirect |
| 23. #63547 | C4 | semidirect |
| 24. #63545 | C4 | semidirect |
| 29. #4895 | D3 | semidirect |
| 35. #4497 | D3 | semidirect |
| 265. C32 | #2179 | semidirect |
| 301. C3 | #69239 | semidirect |
| 302. C3 | #70922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4895 | 2 |
| #10590915 | 2 |
| #10590629 | 2 |
| #10589359 | 2 |
| C3×#4497 | 2 |
| #10589121 | 2 |
| #10589103 | 2 |
| #70922 | 3 |
| #69239 | 3 |