Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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. #10619507 | C2 | semidirect |
| 12. C3×Q8×C9 | D3 | semidirect |
| 27. C32⋊C9 | SD16 | semidirect |
| 30. C32×Q8 | D9 | semidirect |
| 63. C3×C9 | #215 | semidirect |
| 97. C32 | #3675 | semidirect |
| 100. Q8 | #4181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C32⋊C9 | 2 |
| C4⋊#4181 | 2 |
| #10619507 | 2 |
| C3×#3755 | 3 |
| C3×#3675 | 3 |