Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 9. #16837805 | C4 | semidirect |
| 10. #16837781 | C4 | semidirect |
| 11. #16837754 | C4 | semidirect |
| 12. #16837752 | C4 | semidirect |
| 86. C42×C59 | Q16 | semidirect |
| 181. C59 | #9845 | semidirect |
| 257. C42 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434678 | 2 |
| #21425073 | 2 |
| C42×C59⋊C8 | 2 |
| #21422854 | 2 |
| #21422551 | 2 |
| #21422550 | 2 |
| C59×#1994 | 2 |
| #9845 | 59 |