Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
548 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21424134 | C2 | semidirect |
| 2. C8×C22⋊Dic59 | C2 | semidirect |
| 3. #21422612 | C2 | semidirect |
| 4. #21422456 | C2 | semidirect |
| 15. C22×D8×C59 | C4 | semidirect |
| 22. C2×#107×C59 | C4 | semidirect |
| 23. C2×#102×C59 | C4 | semidirect |
| 176. C22×D8 | Dic59 | semidirect |
| 184. C2×#107 | Dic59 | semidirect |
| 185. C2×#102 | Dic59 | semidirect |
| 194. C59 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424134 | 2 |
| C8×C22⋊Dic59 | 2 |
| #21422612 | 2 |
| #21422456 | 2 |
| C2×C59×#466 | 2 |
| #9815 | 59 |