Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21433190 | C2 | semidirect |
| 3. #21422827 | C2 | semidirect |
| 6. #21422006 | C2 | semidirect |
| 7. C59×#1287 | C2 | semidirect |
| 170. #1287 | D59 | semidirect |
| 197. C59 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434196 | 2 |
| #21433190 | 2 |
| #21422827 | 2 |
| #21422522 | 2 |
| #21422436 | 2 |
| #21422006 | 2 |
| C59×#1287 | 2 |
| #9530 | 59 |