Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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×C8×D263 | C2 | semidirect |
| 3. C2×#22554391 | C2 | semidirect |
| 4. #30681795 | C2 | semidirect |
| 5. #30681701 | C2 | semidirect |
| 6. #30681700 | C2 | semidirect |
| 7. C2×#102×C263 | C2 | semidirect |
| 15. #22554441 | C4 | semidirect |
| 41. C2×C263⋊C8 | D4 | semidirect |
| 60. C2×C8×C263 | D4 | semidirect |
| 127. C2×D263 | #102 | semidirect |
| 145. C263 | #1893 | semidirect |
| 150. C2×#102 | D263 | semidirect |
| 200. C2×C8 | C22⋊D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D263 | 2 |
| C2×#22554441 | 2 |
| C2×#22554391 | 2 |
| #30681795 | 2 |
| #30681701 | 2 |
| #30681700 | 2 |
| C2×#102×C263 | 2 |
| #1893 | 263 |