Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 317 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 |
|---|---|---|
| 2. C3×#4880 | C2 | semidirect |
| 3. C32×#357 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 6. C3×#4504 | C2 | semidirect |
| 7. C3×#4490 | C2 | semidirect |
| 9. #69201 | C3 | direct (N × H) |
| 24. #4880 | C2×C3 | semidirect |
| 29. C3×#357 | D3 | semidirect |
| 30. C3×#357 | C2×C3 | semidirect |
| 32. #4562 | C2×C3 | semidirect |
| 33. (C2×D3)⋊C16 | C2×C3 | semidirect |
| 34. #4504 | C2×C3 | semidirect |
| 35. #4490 | C2×C3 | semidirect |
| 99. #357 | C3×D3 | semidirect |
| 257. C32 | #2234 | semidirect |
| 301. C3 | #69201 | direct (N × H) |
| 302. C3 | C3×#2234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5157 | 2 |
| C3×#4880 | 2 |
| C32×#357 | 2 |
| C3×#4562 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4504 | 2 |
| C3×#4490 | 2 |
| C3×#2234 | 3 |
| #69201 | 3 |