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. #10619608 | C2 | semidirect |
| 4. Q8×C3⋊(C3⋊D3) | C3 | semidirect |
| 9. C33×Q8 | C2×C3 | semidirect |
| 11. #6308 | C2×C3 | semidirect |
| 13. Q8×H(3,𝔽3) | D3 | semidirect |
| 17. #4175 | Q8 | direct (N × H) |
| 29. AΣL(1,𝔽27) | C2×Q8 | semidirect |
| 44. C3⋊(C3⋊D3) | C3×Q8 | semidirect |
| 65. C33 | C2×C3×Q8 | semidirect |
| 67. H(3,𝔽3) | D3×Q8 | semidirect |
| 108. Q8 | #4175 | 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×#4175 | 2 |
| #10619608 | 2 |
| Q8×C3⋊(C3⋊D3) | 3 |
| Q8×(C3⋊D3)⋊C3 | 3 |