Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#16862359 | C2 | semidirect |
| 3. C2×#22554392 | C2 | semidirect |
| 4. C2×#22554390 | C2 | semidirect |
| 5. #30681795 | C2 | semidirect |
| 6. #30681700 | C2 | semidirect |
| 7. #340×C263 | C2 | semidirect |
| 16. #22554445 | C4 | semidirect |
| 48. C2×C263⋊C8 | D4 | semidirect |
| 58. C2×C8×C263 | D4 | semidirect |
| 145. C263 | #1895 | semidirect |
| 153. #340 | D263 | semidirect |
| 200. C2×C8 | D1052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16862359 | 2 |
| C2×#22554445 | 2 |
| C2×#22554392 | 2 |
| C2×#22554390 | 2 |
| #30681795 | 2 |
| #30681700 | 2 |
| #340×C263 | 2 |
| #1895 | 263 |