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×#6891 | C3 | semidirect |
| 3. #11757866 | C3 | semidirect |
| 4. C3×#66368 | C3 | semidirect |
| 5. #11757852 | C3 | semidirect |
| 6. #11757851 | C3 | semidirect |
| 7. #11757851 | C3 | semidirect |
| 8. #11757850 | C3 | semidirect |
| 9. #11757849 | C3 | semidirect |
| 39. #6891 | A4 | semidirect |
| 60. C22×C3×C9 | H(3,𝔽3) | semidirect |
| 76. #1094 | H(3,𝔽3) | semidirect |
| 170. C3×C9 | C22⋊H(3,𝔽3) | semidirect |
| 219. 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×#6891 | 3 |
| #11757866 | 3 |
| C3×#66368 | 3 |
| #11757852 | 3 |
| #11757851 | 3 |
| #11757850 | 3 |
| #11757849 | 3 |
| #10624749 | 4 |