Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #30681896 | C2 | semidirect |
| 4. C2×C4×C263⋊C8 | C2 | semidirect |
| 5. #30681702 | C2 | semidirect |
| 6. #30681698 | C2 | semidirect |
| 9. #22554477 | C4 | semidirect |
| 16. #22554394 | C4 | semidirect |
| 17. #22554391 | C4 | semidirect |
| 24. #104×C263 | C4 | semidirect |
| 98. C263 | #1764 | semidirect |
| 118. #104 | Dic263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554477 | 2 |
| #30681934 | 2 |
| #30681896 | 2 |
| C2×C4×C263⋊C8 | 2 |
| #30681702 | 2 |
| #30681698 | 2 |
| C2×#104×C263 | 2 |
| #1764 | 263 |