Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
304 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 304 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×#732 | C2 | semidirect |
| 3. #10619666 | C2 | semidirect |
| 9. Q8×H(3,𝔽3) | D3 | semidirect |
| 10. C3×Q8×C9 | D3 | semidirect |
| 16. #4185 | Q8 | direct (N × H) |
| 26. #732 | C2×Q8 | semidirect |
| 52. H(3,𝔽3) | D3×Q8 | semidirect |
| 53. C3×C9 | D3×Q8 | semidirect |
| 83. Q8 | #4185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#732 | 2 |
| C4×#4185 | 2 |
| #10619666 | 2 |
| Q8×(C3⋊D3)⋊C3 | 3 |
| C3×Q8×D9 | 3 |