Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
580 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 580 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 |
|---|---|---|
| 3. #21422117 | C2 | semidirect |
| 11. C23×Q8×C59 | C4 | semidirect |
| 14. C59×#395 | C4 | semidirect |
| 19. C59×#380 | C4 | semidirect |
| 178. C23×Q8 | Dic59 | semidirect |
| 183. #395 | Dic59 | semidirect |
| 189. #380 | Dic59 | semidirect |
| 193. C59 | #11898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424084 | 2 |
| #21422417 | 2 |
| #21422117 | 2 |
| C59×#2409 | 2 |
| #11898 | 59 |