Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 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. #41×Dic263 | C2 | semidirect |
| 3. C2×#22554396 | C2 | semidirect |
| 4. #30681911 | C2 | semidirect |
| 5. #30681709 | C2 | semidirect |
| 6. #30681697 | C2 | semidirect |
| 7. #421×C263 | C2 | semidirect |
| 10. #22554500 | C4 | semidirect |
| 12. #22554495 | C4 | semidirect |
| 33. C2×Dic526 | C2×C4 | semidirect |
| 34. C2×D1052 | C2×C4 | semidirect |
| 44. #16862360 | C2×C4 | semidirect |
| 129. C263 | #1906 | semidirect |
| 133. #421 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682736 | 2 |
| #41×Dic263 | 2 |
| C2×#22554396 | 2 |
| #30681911 | 2 |
| #30681709 | 2 |
| #30681697 | 2 |
| #421×C263 | 2 |
| #1906 | 263 |