Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 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. #29506388 | C2 | semidirect |
| 3. #29506317 | C2 | semidirect |
| 4. #29506309 | C2 | semidirect |
| 5. #29506308 | C2 | semidirect |
| 6. C8×Dic479 | C2 | semidirect |
| 7. #131×C479 | C2 | semidirect |
| 9. #21440152 | C4 | semidirect |
| 10. #21440150 | C4 | semidirect |
| 11. #21440149 | C4 | semidirect |
| 12. #21440147 | C4 | semidirect |
| 51. C479 | #443 | semidirect |
| 55. #131 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506402 | 2 |
| #29506388 | 2 |
| #29506317 | 2 |
| #29506309 | 2 |
| #29506308 | 2 |
| C8×Dic479 | 2 |
| #131×C479 | 2 |
| #443 | 479 |