Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
814 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C59⋊#1304 | C2 | semidirect |
| 7. C22×C22⋊C4×C59 | C4 | semidirect |
| 9. C59×#381 | C4 | semidirect |
| 106. C22×C22⋊C4 | Dic59 | semidirect |
| 109. #381 | Dic59 | semidirect |
| 112. C59 | #8747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424011 | 2 |
| C59⋊#1304 | 2 |
| C59×#2308 | 2 |
| #8747 | 59 |