Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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. #30681896 | C2 | semidirect |
| 5. C2×#22554380 | C2 | semidirect |
| 6. #30681699 | C2 | semidirect |
| 7. #341×C263 | C2 | semidirect |
| 10. #22554478 | C4 | semidirect |
| 16. #22554396 | C4 | semidirect |
| 17. #22554395 | C4 | semidirect |
| 18. #22554392 | C4 | semidirect |
| 98. C263 | #1765 | semidirect |
| 105. #341 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554478 | 2 |
| C2×#22554396 | 2 |
| #30681935 | 2 |
| #30681896 | 2 |
| C2×#22554380 | 2 |
| #30681699 | 2 |
| #341×C263 | 2 |
| #1765 | 263 |