Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 6. #20294105 | C4 | semidirect |
| 9. C4⋊#13181884 | C4 | semidirect |
| 12. C4⋊Dic433 | C4 | semidirect |
| 14. C4⋊C4×C433 | C4 | semidirect |
| 51. C433 | #340 | semidirect |
| 66. C4⋊C4 | #13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294105 | 2 |
| C2×C4⋊#13181884 | 2 |
| C4⋊C4×D433 | 2 |
| #340 | 433 |