Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
335 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 110 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×#334 | C2 | semidirect |
| 5. C3×#4481 | C2 | semidirect |
| 7. #68543 | C3 | direct (N × H) |
| 24. #4682 | C2×C3 | semidirect |
| 26. C3×#334 | D3 | semidirect |
| 27. C3×#334 | C2×C3 | semidirect |
| 29. #4481 | C2×C3 | semidirect |
| 85. #334 | C3×D3 | semidirect |
| 214. C32 | #1695 | semidirect |
| 251. C3 | #68543 | direct (N × H) |
| 252. C3 | C3×#1695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4842 | 2 |
| C3×#4688 | 2 |
| C3×#4682 | 2 |
| C32×#334 | 2 |
| C3×#4481 | 2 |
| C3×#1695 | 3 |
| #68543 | 3 |