Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
788 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 167 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. #16837425 | C4 | semidirect |
| 12. M16×Dic59 | C4 | semidirect |
| 14. #16837253 | C4 | semidirect |
| 17. #16837247 | C4 | semidirect |
| 154. C59 | #8048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432725 | 2 |
| C4×#14273683 | 2 |
| #21421982 | 2 |
| #21421981 | 2 |
| C59×#1297 | 2 |
| #8048 | 59 |