Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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. #30682341 | C2 | semidirect |
| 4. #30681688 | C2 | semidirect |
| 5. #30681685 | C2 | semidirect |
| 6. #30681684 | C2 | semidirect |
| 48. C263⋊C8 | SD16 | semidirect |
| 78. C263 | #1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682341 | 2 |
| #30682143 | 2 |
| #30682016 | 2 |
| #30681688 | 2 |
| #30681685 | 2 |
| #30681684 | 2 |
| #461×C263 | 2 |
| #1693 | 263 |