Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
974 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 974 conjugacy classes of subgroups — too many to draw. Only its 226 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. #13131738 | C2 | semidirect |
| 2. #13131276 | C2 | semidirect |
| 4. #13130228 | C2 | semidirect |
| 5. #13130219 | C2 | semidirect |
| 9. D4×Q8×C13 | C4 | semidirect |
| 13. #11719426 | C4 | semidirect |
| 17. #11719275 | C4 | semidirect |
| 19. #11719247 | C4 | semidirect |
| 166. D4×Q8 | #261 | semidirect |
| 300. C13 | #17549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131738 | 2 |
| #13131276 | 2 |
| #13130238 | 2 |
| #13130228 | 2 |
| #13130219 | 2 |
| #13130207 | 2 |
| #13128927 | 2 |
| #17549 | 13 |