Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 4. #21422698 | C2 | semidirect |
| 5. #21422608 | C2 | semidirect |
| 6. #21421988 | C2 | semidirect |
| 7. C59×#3236 | C2 | semidirect |
| 174. #3236 | D59 | semidirect |
| 209. C59 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434472 | 2 |
| #21430042 | 2 |
| #21422809 | 2 |
| #21422698 | 2 |
| #21422608 | 2 |
| #21421988 | 2 |
| C59×#3236 | 2 |
| #10097 | 59 |