Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21422711 | C2 | semidirect |
| 5. #21421959 | C2 | semidirect |
| 6. #21421926 | C2 | semidirect |
| 7. C59×#1497 | C2 | semidirect |
| 167. #1497 | D59 | semidirect |
| 196. C59 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435048 | 2 |
| #21433171 | 2 |
| #21422711 | 2 |
| #21422708 | 2 |
| #21421959 | 2 |
| #21421926 | 2 |
| C59×#1497 | 2 |
| #9285 | 59 |