Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30681974 | C2 | semidirect |
| 3. #30681956 | C2 | semidirect |
| 4. #30681955 | C2 | semidirect |
| 5. #30681911 | C2 | semidirect |
| 6. #30681894 | C2 | semidirect |
| 7. #410×C263 | C2 | semidirect |
| 13. C2×#16862366 | C4 | semidirect |
| 14. C2×#16862364 | C4 | semidirect |
| 15. C2×#16862363 | C4 | semidirect |
| 16. C2×#16862361 | C4 | semidirect |
| 132. C263 | #1976 | semidirect |
| 139. #410 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554490 | 2 |
| #30681974 | 2 |
| #30681956 | 2 |
| #30681955 | 2 |
| #30681911 | 2 |
| #30681894 | 2 |
| #410×C263 | 2 |
| #1976 | 263 |