Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
308 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C3×#800 | C2 | semidirect |
| 2. C3×#4901 | C2 | semidirect |
| 4. C3×#4896 | C2 | semidirect |
| 5. C32×#368 | C2 | semidirect |
| 6. C3×#4496 | C2 | semidirect |
| 7. C3×#4495 | C2 | semidirect |
| 9. #69363 | C3 | direct (N × H) |
| 29. C2×#800 | C2×C3 | semidirect |
| 30. #4901 | C2×C3 | semidirect |
| 32. #4896 | C2×C3 | semidirect |
| 34. C3×#368 | D3 | semidirect |
| 35. C3×#368 | C2×C3 | semidirect |
| 38. #4496 | C2×C3 | semidirect |
| 39. #4495 | C2×C3 | semidirect |
| 114. #368 | C3×D3 | semidirect |
| 265. C32 | #2223 | semidirect |
| 301. C3 | #69363 | direct (N × H) |
| 302. C3 | C3×#2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| C3×#4901 | 2 |
| C3×#4897 | 2 |
| C3×#4896 | 2 |
| C32×#368 | 2 |
| C3×#4496 | 2 |
| C3×#4495 | 2 |
| C3×#2223 | 3 |
| #69363 | 3 |