Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. #29506347 | C2 | semidirect |
| 4. #29506305 | C2 | semidirect |
| 6. #29506292 | C2 | semidirect |
| 7. #107×C479 | C2 | semidirect |
| 11. #21440151 | C4 | semidirect |
| 22. Dic958 | C2×C4 | semidirect |
| 33. C8×C479 | C2×C4 | semidirect |
| 49. C479 | #440 | semidirect |
| 54. #107 | D479 | semidirect |
| 83. C8 | C4×D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440151 | 2 |
| #29506347 | 2 |
| #29506344 | 2 |
| #29506305 | 2 |
| #29506302 | 2 |
| #29506292 | 2 |
| #107×C479 | 2 |
| #440 | 479 |