Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #21425717 | C2 | semidirect |
| 2. #21424142 | C2 | semidirect |
| 3. #21422081 | C2 | semidirect |
| 9. #16837184 | C22 | semidirect |
| 10. #16837159 | C22 | semidirect |
| 11. C22×D8×C59 | C4 | semidirect |
| 14. C59×#469 | C4 | semidirect |
| 18. C59×#427 | C4 | semidirect |
| 155. C22×D8 | Dic59 | semidirect |
| 159. #469 | Dic59 | semidirect |
| 164. #427 | Dic59 | semidirect |
| 170. C59 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425717 | 2 |
| #21424142 | 2 |
| #21422081 | 2 |
| C59×#3058 | 2 |
| #11868 | 59 |