Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #30682491 | C2 | semidirect |
| 5. #30681699 | C2 | semidirect |
| 6. #30681695 | C2 | semidirect |
| 7. #344×C263 | C2 | semidirect |
| 28. C2×Dic526 | Q8 | semidirect |
| 29. C2×D1052 | Q8 | semidirect |
| 102. C263 | #2031 | semidirect |
| 108. #344 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682491 | 2 |
| #30681954 | 2 |
| C2×#22554396 | 2 |
| #30681911 | 2 |
| #30681699 | 2 |
| #30681695 | 2 |
| #344×C263 | 2 |
| #2031 | 263 |