Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21422647 | C2 | semidirect |
| 4. #21422517 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 26. C59×#501 | C4 | semidirect |
| 27. C59×#501 | C4 | semidirect |
| 28. C59×#489 | C4 | semidirect |
| 29. C59×#489 | C4 | semidirect |
| 199. #501 | Dic59 | semidirect |
| 200. #501 | Dic59 | semidirect |
| 201. #489 | Dic59 | semidirect |
| 202. #489 | Dic59 | semidirect |
| 224. C59 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433083 | 2 |
| #21422673 | 2 |
| #21422647 | 2 |
| #21422517 | 2 |
| #21421962 | 2 |
| #21421957 | 2 |
| C59×#3240 | 2 |
| #9369 | 59 |