Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
332 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
| 2. C4⋊#4174 | C2 | semidirect |
| 3. C4×#4174 | C2 | semidirect |
| 5. #88748 | C3 | semidirect |
| 9. C33×Q8 | D3 | semidirect |
| 13. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C4⋊#272 | C2×C3 | semidirect |
| 15. C4×#272 | C2×C3 | semidirect |
| 29. AΣL(1,𝔽27) | #41 | semidirect |
| 65. C33 | #239 | semidirect |
| 67. H(3,𝔽3) | C3×#41 | semidirect |
| 107. Q8 | #4174 | semidirect |
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 |
| C4×#4174 | 2 |
| C32×#239 | 3 |
| #88748 | 3 |