Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #21423896 | C2 | semidirect |
| 3. #21422219 | C2 | semidirect |
| 4. #21422217 | C2 | semidirect |
| 9. #16837192 | C4 | semidirect |
| 10. #16837189 | C4 | semidirect |
| 13. C22×M16×C59 | C4 | semidirect |
| 17. C59×#424 | C4 | semidirect |
| 19. C59×#407 | C4 | semidirect |
| 20. C59×#405 | C4 | semidirect |
| 149. C22×M16 | Dic59 | semidirect |
| 153. #424 | Dic59 | semidirect |
| 157. #407 | Dic59 | semidirect |
| 159. #405 | Dic59 | semidirect |
| 163. C59 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425737 | 2 |
| #21423896 | 2 |
| #21422219 | 2 |
| #21422217 | 2 |
| C59×#2930 | 2 |
| #12624 | 59 |