Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
289 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 289 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. #10589360 | C2 | semidirect |
| 4. C3×#4495 | C2 | semidirect |
| 5. #10589137 | C2 | semidirect |
| 6. #10589126 | C2 | semidirect |
| 7. #10589109 | C2 | semidirect |
| 24. #4893 | D3 | semidirect |
| 31. #4495 | D3 | semidirect |
| 240. C32 | #2238 | semidirect |
| 277. C3 | #69257 | semidirect |
| 278. 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 |
| #10590836 | 2 |
| #10589360 | 2 |
| C3×#4495 | 2 |
| #10589137 | 2 |
| #10589126 | 2 |
| #10589109 | 2 |
| #70723 | 3 |
| #69257 | 3 |