Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
518 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21422822 | C2 | semidirect |
| 5. #21421953 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1558 | C2 | semidirect |
| 190. #1558 | D59 | semidirect |
| 222. C59 | #9451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433124 | 2 |
| #21429092 | 2 |
| #21422822 | 2 |
| #21422436 | 2 |
| #21421953 | 2 |
| #21421951 | 2 |
| C59×#1558 | 2 |
| #9451 | 59 |