Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22554476 | C2 | semidirect |
| 3. C2×#22554397 | C2 | semidirect |
| 4. C2×#22554396 | C2 | semidirect |
| 5. #30681702 | C2 | semidirect |
| 6. #30681692 | C2 | semidirect |
| 7. #408×C263 | C2 | semidirect |
| 11. C2×#16862366 | C4 | semidirect |
| 12. C2×#16862364 | C4 | semidirect |
| 13. C2×#16862363 | C4 | semidirect |
| 14. C2×#16862361 | C4 | semidirect |
| 130. C263 | #1876 | semidirect |
| 136. #408 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554490 | 2 |
| C2×#22554476 | 2 |
| C2×#22554397 | 2 |
| C2×#22554396 | 2 |
| #30681702 | 2 |
| #30681692 | 2 |
| #408×C263 | 2 |
| #1876 | 263 |