Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 359 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 |
|---|---|---|
| 2. C3×#4699 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C3×#4486 | C2 | semidirect |
| 7. #68541 | C3 | direct (N × H) |
| 23. #4699 | C2×C3 | semidirect |
| 26. C3×#334 | D3 | semidirect |
| 27. C3×#334 | C2×C3 | semidirect |
| 29. #4486 | C2×C3 | semidirect |
| 88. #334 | C3×D3 | semidirect |
| 225. C32 | #1689 | semidirect |
| 263. C3 | #68541 | direct (N × H) |
| 264. C3 | C3×#1689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4846 | 2 |
| C3×#4699 | 2 |
| C3×#4688 | 2 |
| C32×#334 | 2 |
| C3×#4486 | 2 |
| C3×#1689 | 3 |
| #68541 | 3 |