Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
438 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 186 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. C32×Q8×C9 | C2 | semidirect |
| 3. C32×Dic18 | C2 | semidirect |
| 5. C3×Q8×D9 | C3 | direct (N × H) |
| 13. C3×Q8×C9 | C2×C3 | semidirect |
| 15. C3×Dic18 | C2×C3 | semidirect |
| 17. C32×D9 | Q8 | direct (N × H) |
| 20. Q8×D9 | C32 | direct (N × H) |
| 28. C32×C9 | C2×Q8 | semidirect |
| 31. C32×Q8 | D9 | direct (N × H) |
| 37. Q8×C9 | C2×C32 | semidirect |
| 39. Dic18 | C2×C32 | semidirect |
| 44. C3×D9 | C3×Q8 | direct (N × H) |
| 60. C3×C9 | C2×C3×Q8 | semidirect |
| 63. C3×Q8 | C3×D9 | direct (N × H) |
| 75. D9 | C32×Q8 | direct (N × H) |
| 85. C32 | Q8×D9 | direct (N × H) |
| 88. C9 | C2×C32×Q8 | semidirect |
| 90. Q8 | C32×D9 | direct (N × H) |
| 101. C3 | C3×Q8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C32×C4×D9 | 2 |
| C32×Dic18 | 2 |
| C32×D3×Q8 | 3 |
| C3×Q8×D9 | 3 |