Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
316 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 62 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×AΣL(1,𝔽27) | C2 | semidirect |
| 3. #10619607 | C2 | semidirect |
| 5. Q8×#272 | C3 | semidirect |
| 9. C33×Q8 | D3 | semidirect |
| 13. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 15. #6229 | C2×C3 | semidirect |
| 17. #4174 | Q8 | direct (N × H) |
| 29. AΣL(1,𝔽27) | C2×Q8 | semidirect |
| 47. #272 | C3×Q8 | semidirect |
| 65. C33 | D3×Q8 | semidirect |
| 67. H(3,𝔽3) | C2×C3×Q8 | semidirect |
| 108. Q8 | #4174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×AΣL(1,𝔽27) | 2 |
| C4×#4174 | 2 |
| #10619607 | 2 |
| C32×D3×Q8 | 3 |
| Q8×#272 | 3 |