Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. #30682311 | C2 | semidirect |
| 3. #30682233 | C2 | semidirect |
| 4. #30682229 | C2 | semidirect |
| 5. #30681681 | C2 | semidirect |
| 6. #30681667 | C2 | semidirect |
| 7. Q8⋊C8×C263 | C2 | semidirect |
| 69. Q8×C263 | SD16 | semidirect |
| 98. C263 | #1631 | semidirect |
| 105. Q8⋊C8 | D263 | semidirect |
| 153. Q8 | #16862365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682610 | 2 |
| #30682311 | 2 |
| #30682233 | 2 |
| #30682229 | 2 |
| #30681681 | 2 |
| #30681667 | 2 |
| Q8⋊C8×C263 | 2 |
| #1631 | 263 |