Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4699 | C2 | semidirect |
| 4. #10589323 | C2 | semidirect |
| 5. #10589093 | C2 | semidirect |
| 23. #4699 | D3 | semidirect |
| 225. C32 | #1689 | semidirect |
| 263. C3 | #70871 | semidirect |
| 264. C3 | #71306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4688 | 2 |
| #10590269 | 2 |
| #10589323 | 2 |
| #10589093 | 2 |
| #71306 | 3 |
| #70871 | 3 |