Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4858 | C2 | semidirect |
| 3. #10589353 | C2 | semidirect |
| 5. #10589136 | C2 | semidirect |
| 6. #10589134 | C2 | semidirect |
| 23. #4858 | D3 | semidirect |
| 223. C32 | #2231 | semidirect |
| 254. C3 | #69247 | semidirect |
| 255. C3 | #71358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4858 | 2 |
| #10590915 | 2 |
| #10589353 | 2 |
| C3×#4488 | 2 |
| #10589136 | 2 |
| #10589134 | 2 |
| #10589123 | 2 |
| #71358 | 3 |
| #69247 | 3 |