Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #29506377 | C2 | semidirect |
| 2. #29506375 | C2 | semidirect |
| 3. #29506372 | C2 | semidirect |
| 4. #29506368 | C2 | semidirect |
| 5. #29506366 | C2 | semidirect |
| 6. #29506363 | C2 | semidirect |
| 7. #29506359 | C2 | semidirect |
| 9. C4×Dic958 | C2 | semidirect |
| 10. C4×C22⋊D479 | C2 | semidirect |
| 11. C4×C22⋊D479 | C2 | semidirect |
| 12. #29506341 | C2 | semidirect |
| 13. #29506339 | C2 | semidirect |
| 14. C2×C4×Dic479 | C2 | semidirect |
| 15. C4×D4×C479 | C2 | semidirect |
| 103. C479 | #529 | semidirect |
| 116. C4×D4 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506377 | 2 |
| #29506375 | 2 |
| #29506372 | 2 |
| #29506368 | 2 |
| #29506366 | 2 |
| #29506363 | 2 |
| #29506359 | 2 |
| #29506354 | 2 |
| C4×Dic958 | 2 |
| C4×C22⋊D479 | 2 |
| #29506341 | 2 |
| #29506339 | 2 |
| C2×C4×Dic479 | 2 |
| C4×D4×C479 | 2 |
| #529 | 479 |