Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #21422647 | C2 | semidirect |
| 5. #21421967 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 7. C59×#1537 | C2 | semidirect |
| 9. #16837805 | C4 | semidirect |
| 10. #16837776 | C4 | semidirect |
| 11. #16837752 | C4 | semidirect |
| 12. #16837750 | C4 | semidirect |
| 157. #1537 | D59 | semidirect |
| 186. C59 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434815 | 2 |
| #21433166 | 2 |
| #21422647 | 2 |
| #21422644 | 2 |
| #21421967 | 2 |
| #21421962 | 2 |
| C59×#1537 | 2 |
| #9415 | 59 |