Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 2. #30681986 | C2 | semidirect |
| 4. #30681946 | C2 | semidirect |
| 6. C2×#22554388 | C2 | semidirect |
| 7. #344×C263 | C2 | semidirect |
| 105. C263 | #2049 | semidirect |
| 113. #344 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554503 | 2 |
| #30681986 | 2 |
| #30681956 | 2 |
| #30681946 | 2 |
| #30681920 | 2 |
| C2×#22554388 | 2 |
| #344×C263 | 2 |
| #2049 | 263 |