Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
204 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 204 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. Q8×#737 | C2 | semidirect |
| 3. #10619724 | C2 | semidirect |
| 4. #88548 | C3 | semidirect |
| 13. Q8×3−1+2 | D3 | semidirect |
| 16. C3×Q8×C9 | D3 | semidirect |
| 17. C3×Q8×C9 | C2×C3 | semidirect |
| 22. C3⋊(C9⋊C8) | C2×C3 | semidirect |
| 50. #737 | SD16 | semidirect |
| 100. 3−1+2 | #215 | semidirect |
| 103. C3×C9 | #215 | semidirect |
| 104. C3×C9 | C3×SD16 | semidirect |
| 145. Q8 | #4207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#737 | 2 |
| C4⋊#4207 | 2 |
| #10619724 | 2 |
| #88548 | 3 |
| #3675⋊C3 | 3 |
| #3755⋊C3 | 3 |
| C3×#3675 | 3 |