Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21425869 | C2 | semidirect |
| 4. #21424887 | C2 | semidirect |
| 5. #21422210 | C2 | semidirect |
| 6. #21422183 | C2 | semidirect |
| 23. C59×#361 | C4 | semidirect |
| 52. M32×C59 | C2×C4 | semidirect |
| 55. #108×C59 | C2×C4 | semidirect |
| 159. #361 | Dic59 | semidirect |
| 161. C59 | #12953 | semidirect |
| 181. M32 | C2×Dic59 | semidirect |
| 188. #108 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432948 | 2 |
| #21425869 | 2 |
| C2×#16837215 | 2 |
| #21424887 | 2 |
| #21422210 | 2 |
| #21422183 | 2 |
| C2×C59×#361 | 2 |
| #12953 | 59 |