Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
590 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
| 172. C23×Q8 | Dic59 | semidirect |
| 177. #395 | Dic59 | semidirect |
| 182. #380 | Dic59 | semidirect |
| 187. C59 | #11785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273642 | 2 |
| #21422437 | 2 |
| #21422117 | 2 |
| C59×#2409 | 2 |
| #11785 | 59 |