Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #30682413 | C2 | semidirect |
| 3. #30681954 | C2 | semidirect |
| 4. #30681911 | C2 | semidirect |
| 5. #30681710 | C2 | semidirect |
| 6. #30681694 | C2 | semidirect |
| 7. #418×C263 | C2 | semidirect |
| 11. C2×#16862364 | C4 | semidirect |
| 12. C2×#16862361 | C4 | semidirect |
| 29. C2×Dic526 | C2×C4 | semidirect |
| 30. C2×D1052 | C2×C4 | semidirect |
| 38. C2×C263⋊C8 | C2×C4 | semidirect |
| 115. C263 | #1904 | semidirect |
| 120. #418 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554496 | 2 |
| #30682413 | 2 |
| #30681954 | 2 |
| #30681911 | 2 |
| #30681710 | 2 |
| #30681694 | 2 |
| #418×C263 | 2 |
| #1904 | 263 |