Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
347 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 114 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×#4682 | C2 | semidirect |
| 4. C32×#335 | C2 | semidirect |
| 5. C3×#4481 | C2 | semidirect |
| 7. #68579 | C3 | direct (N × H) |
| 24. #4682 | C2×C3 | semidirect |
| 26. C3×#335 | D3 | semidirect |
| 27. C3×#335 | C2×C3 | semidirect |
| 29. #4481 | C2×C3 | semidirect |
| 86. #335 | C3×D3 | semidirect |
| 221. C32 | #1675 | semidirect |
| 260. C3 | #68579 | direct (N × H) |
| 261. C3 | C3×#1675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4842 | 2 |
| C3×C8×D12 | 2 |
| C3×#4682 | 2 |
| C32×#335 | 2 |
| C3×#4481 | 2 |
| C3×#1675 | 3 |
| #68579 | 3 |