Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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. #30681893 | C2 | semidirect |
| 5. #30681703 | C2 | semidirect |
| 6. #30681698 | C2 | semidirect |
| 7. C2×#97×C263 | C2 | semidirect |
| 10. #22554476 | C4 | semidirect |
| 16. #22554398 | C4 | semidirect |
| 17. #22554395 | C4 | semidirect |
| 18. #22554392 | C4 | semidirect |
| 98. C263 | #1765 | semidirect |
| 104. C2×#97 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554476 | 2 |
| C2×#22554398 | 2 |
| #30681935 | 2 |
| #30681893 | 2 |
| #30681703 | 2 |
| #30681698 | 2 |
| C2×#97×C263 | 2 |
| #1765 | 263 |