Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #21434628 | C2 | semidirect |
| 5. #21422201 | C2 | semidirect |
| 6. #21422183 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 30. C2×Dic236 | Q8 | semidirect |
| 32. C2×D472 | Q8 | semidirect |
| 157. #1384 | D59 | semidirect |
| 181. C59 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434628 | 2 |
| #21425831 | 2 |
| C2×#16837213 | 2 |
| #21424992 | 2 |
| #21422201 | 2 |
| #21422183 | 2 |
| C59×#1384 | 2 |
| #13374 | 59 |