Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
318 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 131 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. #16837228 | C4 | semidirect |
| 55. C16×C59 | C4⋊C4 | semidirect |
| 111. C59 | #13168 | semidirect |
| 152. C16 | Dic59⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837228 | 2 |
| C2×#16837177 | 2 |
| #21424827 | 2 |
| #21422187 | 2 |
| C2×C59×#367 | 2 |
| #13168 | 59 |