Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 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. #21424869 | C2 | semidirect |
| 5. #21422386 | C2 | semidirect |
| 6. #21421937 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 16. #16837147 | C4 | semidirect |
| 17. #16837147 | C4 | semidirect |
| 18. #16837145 | C4 | semidirect |
| 19. #16837145 | C4 | semidirect |
| 169. #1303 | D59 | semidirect |
| 196. C59 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425014 | 2 |
| #21424869 | 2 |
| #21422743 | 2 |
| #21422546 | 2 |
| #21422386 | 2 |
| #21421937 | 2 |
| C59×#1303 | 2 |
| #9592 | 59 |