Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
266 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 61 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×#731 | C2 | semidirect |
| 3. #10619663 | C2 | semidirect |
| 10. Q8×3−1+2 | D3 | semidirect |
| 12. C3×Q8×C9 | D3 | semidirect |
| 20. #4184 | Q8 | direct (N × H) |
| 34. #731 | C2×Q8 | semidirect |
| 68. 3−1+2 | D3×Q8 | semidirect |
| 70. C3×C9 | D3×Q8 | semidirect |
| 103. Q8 | #4184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#731 | 2 |
| C4×#4184 | 2 |
| #10619663 | 2 |
| Q8×AGL(1,ℤ/9) | 3 |
| Q8×(C3⋊D3)⋊C3 | 3 |
| C3×Q8×D9 | 3 |