Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #30681708 | C2 | semidirect |
| 5. #30681698 | C2 | semidirect |
| 6. #30681694 | C2 | semidirect |
| 7. #533×C263 | C2 | semidirect |
| 27. C2×Dic526 | Q8 | semidirect |
| 28. C2×D1052 | Q8 | semidirect |
| 101. C263 | #2031 | semidirect |
| 103. #533 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30681956 | 2 |
| C2×#22554398 | 2 |
| #30681911 | 2 |
| #30681708 | 2 |
| #30681698 | 2 |
| #30681694 | 2 |
| #533×C263 | 2 |
| #2031 | 263 |