Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 50. C263⋊C8 | Q16 | semidirect |
| 72. C263 | #1694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682341 | 2 |
| #30682149 | 2 |
| #30682145 | 2 |
| #30682065 | 2 |
| #30681688 | 2 |
| #30681683 | 2 |
| #332×C263 | 2 |
| #1694 | 263 |