Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #21425770 | C2 | semidirect |
| 4. #21425751 | C2 | semidirect |
| 6. #21424142 | C2 | semidirect |
| 7. C59×#1757 | C2 | semidirect |
| 8. C22×#11745660 | C4 | semidirect |
| 16. #16837440 | C4 | semidirect |
| 17. #16837412 | C4 | semidirect |
| 18. #16837408 | C4 | semidirect |
| 213. #1757 | D59 | semidirect |
| 243. C59 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433735 | 2 |
| #21425770 | 2 |
| #21425767 | 2 |
| #21425751 | 2 |
| #21425747 | 2 |
| #21424142 | 2 |
| C59×#1757 | 2 |
| #13229 | 59 |