Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 4. #30681894 | C2 | semidirect |
| 5. #30681707 | C2 | semidirect |
| 6. #30681702 | C2 | semidirect |
| 7. #428×C263 | C2 | semidirect |
| 16. #22554386 | C4 | semidirect |
| 100. C263 | #1931 | semidirect |
| 102. #428 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681942 | 2 |
| C2×#22554390 | 2 |
| C2×#22554386 | 2 |
| #30681894 | 2 |
| #30681707 | 2 |
| #30681702 | 2 |
| #428×C263 | 2 |
| #1931 | 263 |