Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 273 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×#4855 | C2 | semidirect |
| 3. #10589353 | C2 | semidirect |
| 5. #10589136 | C2 | semidirect |
| 6. #10589134 | C2 | semidirect |
| 23. #4855 | D3 | semidirect |
| 45. C3×Dic12 | Q8 | semidirect |
| 46. C3×D24 | Q8 | semidirect |
| 125. Dic12 | Dic6 | semidirect |
| 126. D24 | Dic6 | semidirect |
| 226. C32 | #2230 | semidirect |
| 258. C3 | #69246 | semidirect |
| 259. C3 | #71350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4855 | 2 |
| #10590915 | 2 |
| #10589353 | 2 |
| C3×#4488 | 2 |
| #10589136 | 2 |
| #10589134 | 2 |
| #10589123 | 2 |
| #71350 | 3 |
| #69246 | 3 |