Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
380 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 380 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×AΣL(1,𝔽27) | C2 | semidirect |
| 3. #10619660 | C2 | semidirect |
| 10. C33×Q8 | D3 | semidirect |
| 13. Q8×3−1+2 | D3 | semidirect |
| 14. Q8×H(3,𝔽3) | D3 | semidirect |
| 20. #4183 | Q8 | direct (N × H) |
| 35. AΣL(1,𝔽27) | C2×Q8 | semidirect |
| 76. C33 | D3×Q8 | semidirect |
| 77. 3−1+2 | D3×Q8 | semidirect |
| 78. H(3,𝔽3) | D3×Q8 | semidirect |
| 120. Q8 | #4183 | 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×#4183 | 2 |
| #10619660 | 2 |
| C3×Q8×C3⋊D3 | 3 |
| Q8×AGL(1,ℤ/9) | 3 |
| Q8×(C3⋊D3)⋊C3 | 3 |