Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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. #30682566 | C2 | semidirect |
| 4. #30681706 | C2 | semidirect |
| 5. #30681699 | C2 | semidirect |
| 6. #30681697 | C2 | semidirect |
| 49. C2×D4×C263 | Q8 | semidirect |
| 112. C263 | #2027 | semidirect |
| 145. C2×D4 | Dic526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682566 | 2 |
| #30681943 | 2 |
| #30681841 | 2 |
| #30681706 | 2 |
| #30681699 | 2 |
| #30681697 | 2 |
| #418×C263 | 2 |
| #2027 | 263 |