Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
231 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 78 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. C32×#334 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 5. #67467 | C3 | direct (N × H) |
| 17. C3×#334 | D3 | semidirect |
| 18. C3×#334 | C2×C3 | semidirect |
| 19. C4⋊(C3⋊C16) | C2×C3 | semidirect |
| 65. #334 | C3×D3 | semidirect |
| 185. C32 | #1360 | semidirect |
| 220. C3 | #67467 | direct (N × H) |
| 221. C3 | C3×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| C32×#334 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#1360 | 3 |
| #67467 | 3 |