Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 568 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. #21423829 | C2 | semidirect |
| 2. #21422410 | C2 | semidirect |
| 3. #21422093 | C2 | semidirect |
| 11. C2×#127×C59 | C4 | semidirect |
| 15. C59×#394 | C4 | semidirect |
| 19. C59×#382 | C4 | semidirect |
| 182. C2×#127 | Dic59 | semidirect |
| 188. #394 | Dic59 | semidirect |
| 192. #382 | Dic59 | semidirect |
| 197. C59 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21423829 | 2 |
| #21422410 | 2 |
| #21422093 | 2 |
| C59×#2619 | 2 |
| #11693 | 59 |