Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #29506429 | C2 | semidirect |
| 2. #29506428 | C2 | semidirect |
| 3. #29506415 | C2 | semidirect |
| 4. #29506410 | C2 | semidirect |
| 5. #29506404 | C2 | semidirect |
| 6. C2×#21440151 | C2 | semidirect |
| 7. #131×C479 | C2 | semidirect |
| 10. #21440162 | C22 | semidirect |
| 12. C2×Dic958 | C22 | semidirect |
| 16. Dic1916 | C22 | semidirect |
| 17. #21440151 | C22 | semidirect |
| 18. #21440151 | C22 | semidirect |
| 19. #21440151 | C22 | semidirect |
| 20. D3832 | C22 | semidirect |
| 22. M16×C479 | C22 | semidirect |
| 23. C2×C8×C479 | C22 | semidirect |
| 53. C479 | #577 | semidirect |
| 61. #131 | D479 | semidirect |
| 76. M16 | C2×D479 | semidirect |
| 77. C2×C8 | C2×D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506429 | 2 |
| #29506428 | 2 |
| #29506415 | 2 |
| #29506410 | 2 |
| #29506404 | 2 |
| C2×#21440151 | 2 |
| #131×C479 | 2 |
| #577 | 479 |