Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 12. #22554403 | C4 | semidirect |
| 13. #22554403 | C4 | semidirect |
| 14. #22554401 | C4 | semidirect |
| 15. #22554401 | C4 | semidirect |
| 88. C263 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681974 | 2 |
| #30681893 | 2 |
| #30681702 | 2 |
| #30681699 | 2 |
| #30681697 | 2 |
| #30681692 | 2 |
| #424×C263 | 2 |
| #1922 | 263 |