Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#16837197 | C2 | semidirect |
| 2. #21422720 | C2 | semidirect |
| 3. #21422247 | C2 | semidirect |
| 8. #16837197 | C22 | semidirect |
| 10. #16837142 | C22 | semidirect |
| 11. C2×2−1+4×C59 | C4 | semidirect |
| 16. C59×#454 | C4 | semidirect |
| 19. C2×#101×C59 | C4 | semidirect |
| 29. 2−1+4×C59 | C2×C4 | semidirect |
| 52. #101×C59 | C2×C4 | semidirect |
| 181. C2×2−1+4 | Dic59 | semidirect |
| 186. #454 | Dic59 | semidirect |
| 190. C2×#101 | Dic59 | semidirect |
| 196. C59 | #13569 | semidirect |
| 200. 2−1+4 | C2×Dic59 | semidirect |
| 225. #101 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837197 | 2 |
| #21422720 | 2 |
| #21422247 | 2 |
| C2×C59×#454 | 2 |
| #13569 | 59 |