Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21425882 | C2 | semidirect |
| 5. #21423978 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 17. #16837214 | C4 | semidirect |
| 149. #1387 | D59 | semidirect |
| 173. C59 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425882 | 2 |
| C2×#16837214 | 2 |
| #21425813 | 2 |
| #21424960 | 2 |
| #21423978 | 2 |
| #21422177 | 2 |
| C59×#1387 | 2 |
| #13136 | 59 |