Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
614 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 614 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. #11758104 | C3 | semidirect |
| 2. C22×C3×AΣL(1,𝔽27) | C3 | semidirect |
| 3. #11757866 | C3 | semidirect |
| 4. C3×#66368 | C3 | semidirect |
| 5. #11757864 | C3 | semidirect |
| 6. #11757851 | C3 | semidirect |
| 7. #11757851 | C3 | semidirect |
| 8. #11757850 | C3 | semidirect |
| 9. #11757850 | C3 | semidirect |
| 10. #11757849 | C3 | semidirect |
| 11. #11757841 | C3 | semidirect |
| 12. #11757837 | C3 | semidirect |
| 13. #11757836 | C3 | semidirect |
| 55. C3×AΣL(1,𝔽27) | A4 | semidirect |
| 79. C22×3−1+2 | H(3,𝔽3) | semidirect |
| 112. #1094 | H(3,𝔽3) | semidirect |
| 117. C3×C22⋊C9 | H(3,𝔽3) | semidirect |
| 228. 3−1+2 | C22⋊H(3,𝔽3) | semidirect |
| 316. C22 | #10624749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758104 | 3 |
| C22×C3×AΣL(1,𝔽27) | 3 |
| #11757866 | 3 |
| C3×#66368 | 3 |
| #11757864 | 3 |
| #11757851 | 3 |
| #11757850 | 3 |
| #11757849 | 3 |
| #11757841 | 3 |
| #11757837 | 3 |
| #11757836 | 3 |
| #10624749 | 4 |