Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
684 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 25. C22×Dic118 | Q8 | semidirect |
| 222. C59 | #10341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21430210 | 2 |
| #21424032 | 2 |
| #21422366 | 2 |
| #21421976 | 2 |
| C59×#1280 | 2 |
| #10341 | 59 |