Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
320 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21425785 | C2 | semidirect |
| 2. #21425771 | C2 | semidirect |
| 3. #21422271 | C2 | semidirect |
| 4. #21422253 | C2 | semidirect |
| 12. C59×#540 | C4 | semidirect |
| 15. C59×#492 | C4 | semidirect |
| 16. C59×#491 | C4 | semidirect |
| 22. C59×#433 | C4 | semidirect |
| 154. #540 | Dic59 | semidirect |
| 157. #492 | Dic59 | semidirect |
| 158. #491 | Dic59 | semidirect |
| 164. #433 | Dic59 | semidirect |
| 171. C59 | #13606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425785 | 2 |
| #21425771 | 2 |
| #21422271 | 2 |
| #21422253 | 2 |
| C59×#3221 | 2 |
| #13606 | 59 |