Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 3. #21422712 | C2 | semidirect |
| 5. #21422518 | C2 | semidirect |
| 6. #21421994 | C2 | semidirect |
| 7. C59×#1291 | C2 | semidirect |
| 183. #1291 | D59 | semidirect |
| 212. C59 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434259 | 2 |
| #21432748 | 2 |
| #21422712 | 2 |
| #21422528 | 2 |
| #21422518 | 2 |
| #21421994 | 2 |
| C59×#1291 | 2 |
| #9314 | 59 |