Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 10. #16837123 | C4 | semidirect |
| 11. C8×C59⋊C8 | C4 | semidirect |
| 15. C59×#347 | C4 | semidirect |
| 86. #347 | Dic59 | semidirect |
| 94. C59 | #7226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424245 | 2 |
| #21422393 | 2 |
| C59×#2165 | 2 |
| #7226 | 59 |