Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21423872 | C2 | semidirect |
| 3. #21422617 | C2 | semidirect |
| 5. #21422461 | C2 | semidirect |
| 7. C59×#1810 | C2 | semidirect |
| 8. C22×#11745660 | C4 | semidirect |
| 15. C2×#14273659 | C4 | semidirect |
| 16. C2×#14273652 | C4 | semidirect |
| 17. C2×#14273649 | C4 | semidirect |
| 210. #1810 | D59 | semidirect |
| 246. C59 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837631 | 2 |
| #21423872 | 2 |
| #21422617 | 2 |
| #21422613 | 2 |
| #21422461 | 2 |
| #21422457 | 2 |
| C59×#1810 | 2 |
| #9816 | 59 |