Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425855 | C2 | semidirect |
| 4. #21425700 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 7. C59×#1378 | C2 | semidirect |
| 139. #1378 | D59 | semidirect |
| 160. C59 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425855 | 2 |
| #21425725 | 2 |
| C2×#16837187 | 2 |
| #21425700 | 2 |
| #21423897 | 2 |
| #21422186 | 2 |
| C59×#1378 | 2 |
| #13126 | 59 |