Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
224 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 58 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×C4×#732 | C2 | semidirect |
| 2. #10619649 | C2 | semidirect |
| 3. C4⋊#4178 | C2 | semidirect |
| 4. C4×#4178 | C2 | semidirect |
| 5. #10619619 | C2 | semidirect |
| 6. #88740 | C3 | semidirect |
| 15. C2×C3×C4×C9 | D3 | semidirect |
| 17. C4⋊#272 | C2×C3 | semidirect |
| 18. C4×#272 | C2×C3 | semidirect |
| 19. #6229 | C2×C3 | semidirect |
| 43. #732 | #41 | semidirect |
| 91. C3×C9 | #235 | semidirect |
| 146. C2×C4 | #4178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#732 | 2 |
| #10619649 | 2 |
| C4⋊#4178 | 2 |
| C4×#4178 | 2 |
| #10619619 | 2 |
| #88740 | 3 |
| C9×#235 | 3 |