Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
272 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 19. C59×#367 | C4 | semidirect |
| 20. C59×#366 | C4 | semidirect |
| 138. #367 | Dic59 | semidirect |
| 139. #366 | Dic59 | semidirect |
| 142. C59 | #13118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424835 | 2 |
| #21423982 | 2 |
| #21422204 | 2 |
| #21422201 | 2 |
| #21422195 | 2 |
| #21422175 | 2 |
| C59×#2159 | 2 |
| #13118 | 59 |