Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×#14273660 | C2 | semidirect |
| 3. #21422857 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1285 | C2 | semidirect |
| 9. #16837529 | C4 | semidirect |
| 10. #16837526 | C4 | semidirect |
| 11. #16837479 | C4 | semidirect |
| 13. #16837467 | C4 | semidirect |
| 179. #1285 | D59 | semidirect |
| 209. C59 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433065 | 2 |
| C4×#14273660 | 2 |
| #21422857 | 2 |
| #21422622 | 2 |
| #21422619 | 2 |
| #21421953 | 2 |
| C59×#1285 | 2 |
| #8697 | 59 |