Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. C3×#4492 | C2 | semidirect |
| 4. C3×#4490 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 33. #4492 | D3 | semidirect |
| 35. #4490 | D3 | semidirect |
| 261. C32 | #2235 | semidirect |
| 301. C3 | #69231 | semidirect |
| 302. C3 | #69352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#107 | 2 |
| #10590857 | 2 |
| C3×#4492 | 2 |
| C3×#4490 | 2 |
| #10589141 | 2 |
| #10589118 | 2 |
| #10589108 | 2 |
| #69352 | 3 |
| #69231 | 3 |