Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
656 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21422734 | C2 | semidirect |
| 4. #21422451 | C2 | semidirect |
| 5. C59×#1544 | C2 | semidirect |
| 153. #1544 | D59 | semidirect |
| 180. C59 | #8478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437917 | 2 |
| #21422734 | 2 |
| #21422531 | 2 |
| #21422451 | 2 |
| C59×#1544 | 2 |
| #8478 | 59 |