Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
299 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4893 | C2 | semidirect |
| 3. #10589361 | C2 | semidirect |
| 4. C3×#4494 | C2 | semidirect |
| 5. #10589138 | C2 | semidirect |
| 6. #10589128 | C2 | semidirect |
| 7. #10589109 | C2 | semidirect |
| 23. #4893 | D3 | semidirect |
| 34. #4494 | D3 | semidirect |
| 246. C32 | #2238 | semidirect |
| 284. C3 | #69313 | semidirect |
| 285. C3 | #70723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4893 | 2 |
| #10590835 | 2 |
| #10589361 | 2 |
| C3×#4494 | 2 |
| #10589138 | 2 |
| #10589128 | 2 |
| #10589109 | 2 |
| #70723 | 3 |
| #69313 | 3 |