Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
303 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×#367 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. C3×#4492 | C2 | semidirect |
| 7. C3×#4490 | C2 | semidirect |
| 9. #69352 | C3 | direct (N × H) |
| 27. C3×#367 | D3 | semidirect |
| 28. C3×#367 | C2×C3 | semidirect |
| 33. #4503 | C2×C3 | semidirect |
| 34. #4492 | C2×C3 | semidirect |
| 35. #4490 | C2×C3 | semidirect |
| 97. #367 | C3×D3 | semidirect |
| 244. C32 | #2235 | semidirect |
| 283. C3 | #69352 | direct (N × H) |
| 284. C3 | C3×#2235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4887 | 2 |
| C3×D3×#107 | 2 |
| C32×#367 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#4492 | 2 |
| C3×#4490 | 2 |
| C3×#2235 | 3 |
| #69352 | 3 |