Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
288 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 42 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. C2×#66436 | C2 | semidirect |
| 2. #10620044 | C2 | direct (N × H) |
| 7. #66436 | C22 | semidirect |
| 8. C23×C3×C9 | D3 | semidirect |
| 13. C2×C9×A4 | D3 | semidirect |
| 26. C22×C3×C9 | C2×D3 | semidirect |
| 35. C9×A4 | C2×D3 | semidirect |
| 58. C2×C3×C9 | S4 | semidirect |
| 89. C3×C9 | C2×S4 | semidirect |
| 141. C23 | #4208 | semidirect |
| 162. C22 | C2×#4208 | semidirect |
| 170. C2 | #10620044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66436 | 2 |
| #10620044 | 2 |
| C2×#6258 | 3 |
| C2×C9×S4 | 3 |
| C2×C9×#67 | 3 |
| C2×#4208 | 4 |