Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 11. #22554435 | C4 | semidirect |
| 17. #22554395 | C4 | semidirect |
| 18. #22554393 | C4 | semidirect |
| 57. Dic526 | C42 | semidirect |
| 109. C263 | #1763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554435 | 2 |
| C2×#22554395 | 2 |
| C2×#22554393 | 2 |
| C2×#22554380 | 2 |
| C4⋊C4×Dic263 | 2 |
| #30681700 | 2 |
| #340×C263 | 2 |
| #1763 | 263 |