Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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. #30681845 | C2 | semidirect |
| 5. #30681706 | C2 | semidirect |
| 6. #30681697 | C2 | semidirect |
| 7. #419×C263 | C2 | semidirect |
| 10. #22554501 | C4 | semidirect |
| 42. #16862360 | C2×C4 | semidirect |
| 56. C2×Q8×C263 | C2×C4 | semidirect |
| 124. C263 | #1882 | semidirect |
| 129. #419 | D263 | semidirect |
| 163. C2×Q8 | C4×D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554501 | 2 |
| #30682418 | 2 |
| C2×#22554396 | 2 |
| #30681845 | 2 |
| #30681706 | 2 |
| #30681697 | 2 |
| #419×C263 | 2 |
| #1882 | 263 |