Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
309 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. Q8×C32⋊C9 | C2 | semidirect |
| 3. #10619590 | C2 | semidirect |
| 5. Q8×C3⋊D9 | C3 | semidirect |
| 13. C3×Q8×C9 | C2×C3 | semidirect |
| 15. #6226 | C2×C3 | semidirect |
| 17. #4169 | Q8 | direct (N × H) |
| 30. C32⋊C9 | C2×Q8 | semidirect |
| 34. C32×Q8 | D9 | semidirect |
| 52. C3⋊D9 | C3×Q8 | semidirect |
| 76. C3×C9 | C2×C3×Q8 | semidirect |
| 119. C32 | Q8×D9 | semidirect |
| 124. Q8 | #4169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C32⋊C9 | 2 |
| C4×#4169 | 2 |
| #10619590 | 2 |
| C3×Q8×C3⋊D3 | 3 |
| Q8×C3⋊D9 | 3 |