Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
270 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#22554405 | C2 | semidirect |
| 3. #30681966 | C2 | semidirect |
| 5. #30681698 | C2 | semidirect |
| 6. #30681693 | C2 | semidirect |
| 19. #22554394 | C4 | semidirect |
| 20. #22554394 | C4 | semidirect |
| 21. #22554391 | C4 | semidirect |
| 22. #22554391 | C4 | semidirect |
| 109. C263 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554477 | 2 |
| C2×#22554405 | 2 |
| #30681966 | 2 |
| #30681934 | 2 |
| #30681698 | 2 |
| #30681693 | 2 |
| C2×#104×C263 | 2 |
| #1866 | 263 |