Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 2. C3×#5196 | C2 | semidirect |
| 3. #10590917 | C2 | semidirect |
| 4. C3×#4567 | C2 | semidirect |
| 5. #10589144 | C2 | semidirect |
| 6. #10589122 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 14. #63656 | C4 | semidirect |
| 15. #63655 | C4 | semidirect |
| 16. #63654 | C4 | semidirect |
| 17. #63653 | C4 | semidirect |
| 26. #5196 | D3 | semidirect |
| 33. #4567 | D3 | semidirect |
| 285. C32 | #2179 | semidirect |
| 323. C3 | #69239 | semidirect |
| 324. C3 | #70922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592893 | 2 |
| C3×#5196 | 2 |
| #10590917 | 2 |
| C3×#4567 | 2 |
| #10589144 | 2 |
| #10589122 | 2 |
| #10589103 | 2 |
| #70922 | 3 |
| #69239 | 3 |