Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #21426902 | C2 | semidirect |
| 3. #21422698 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 25. C59×#501 | C4 | semidirect |
| 26. C59×#490 | C4 | semidirect |
| 207. #501 | Dic59 | semidirect |
| 208. #490 | Dic59 | semidirect |
| 228. C59 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426902 | 2 |
| #21425016 | 2 |
| #21422698 | 2 |
| #21422643 | 2 |
| #21421962 | 2 |
| #21421951 | 2 |
| C59×#3234 | 2 |
| #9382 | 59 |