Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #30681691 | C2 | semidirect |
| 4. #30681684 | C2 | semidirect |
| 5. #500×C263 | C2 | semidirect |
| 46. C8×C263 | SD16 | semidirect |
| 62. C263 | #1673 | semidirect |
| 64. #500 | D263 | semidirect |
| 109. C8 | #16862363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682140 | 2 |
| C8×D1052 | 2 |
| #30681691 | 2 |
| #30681684 | 2 |
| #500×C263 | 2 |
| #1673 | 263 |