Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 31. C22×C4×C59 | C16 | semidirect |
| 100. C59 | #7055 | semidirect |
| 124. C22×C4 | C59⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422020 | 2 |
| C59×#1817 | 2 |
| #7055 | 59 |