Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30681986 | C2 | semidirect |
| 4. C4×#16862360 | C2 | semidirect |
| 5. #30681709 | C2 | semidirect |
| 6. #30681698 | C2 | semidirect |
| 14. #22554389 | C4 | semidirect |
| 15. #22554387 | C4 | semidirect |
| 95. C263 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681986 | 2 |
| #30681955 | 2 |
| #30681922 | 2 |
| C4×#16862360 | 2 |
| #30681709 | 2 |
| #30681698 | 2 |
| C2×#104×C263 | 2 |
| #1932 | 263 |