Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 4. #21422570 | C2 | semidirect |
| 5. #21422568 | C2 | semidirect |
| 6. #21421995 | C2 | semidirect |
| 7. C59×#1302 | C2 | semidirect |
| 154. #1302 | D59 | semidirect |
| 179. C59 | #9005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434442 | 2 |
| #21433166 | 2 |
| #21422756 | 2 |
| #21422570 | 2 |
| #21422568 | 2 |
| #21421995 | 2 |
| C59×#1302 | 2 |
| #9005 | 59 |