Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×Dic263⋊C8 | C2 | semidirect |
| 3. C2×#22554392 | C2 | semidirect |
| 4. #30681841 | C2 | semidirect |
| 5. #30681839 | C2 | semidirect |
| 6. #30681700 | C2 | semidirect |
| 7. C2×#102×C263 | C2 | semidirect |
| 80. C2×Dic263 | D8 | semidirect |
| 142. C263 | #2054 | semidirect |
| 147. C2×#102 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16862361 | 2 |
| C2×Dic263⋊C8 | 2 |
| C2×#22554392 | 2 |
| #30681841 | 2 |
| #30681839 | 2 |
| #30681700 | 2 |
| C2×#102×C263 | 2 |
| #2054 | 263 |