Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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. #30681964 | C2 | semidirect |
| 5. #30681703 | C2 | semidirect |
| 6. #30681698 | C2 | semidirect |
| 7. C2×C4×C8×C263 | C2 | semidirect |
| 14. #22554395 | C4 | semidirect |
| 15. #22554392 | C4 | semidirect |
| 90. C263 | #1937 | semidirect |
| 96. C2×C4×C8 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681964 | 2 |
| C2×#22554398 | 2 |
| #30681935 | 2 |
| #30681904 | 2 |
| #30681703 | 2 |
| #30681698 | 2 |
| C2×C4×C8×C263 | 2 |
| #1937 | 263 |