Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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. #30682220 | C2 | semidirect |
| 3. #30682068 | C2 | semidirect |
| 4. #30681691 | C2 | semidirect |
| 5. #30681684 | C2 | semidirect |
| 62. C8×C263 | SD16 | semidirect |
| 79. C263 | #1686 | semidirect |
| 142. C8 | #16862364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682220 | 2 |
| #30682135 | 2 |
| #30682068 | 2 |
| #30681691 | 2 |
| #30681684 | 2 |
| #30681682 | 2 |
| #492×C263 | 2 |
| #1686 | 263 |