Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 1. #21433083 | C2 | semidirect |
| 2. #21422673 | C2 | semidirect |
| 3. #21422643 | C2 | semidirect |
| 4. #21422513 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 26. C59×#497 | C4 | semidirect |
| 27. C59×#496 | C4 | semidirect |
| 28. C59×#491 | C4 | semidirect |
| 29. C59×#490 | C4 | semidirect |
| 214. #497 | Dic59 | semidirect |
| 215. #496 | Dic59 | semidirect |
| 216. #491 | Dic59 | semidirect |
| 217. #490 | Dic59 | semidirect |
| 239. C59 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433083 | 2 |
| #21422673 | 2 |
| #21422643 | 2 |
| #21422513 | 2 |
| #21421962 | 2 |
| #21421957 | 2 |
| C59×#3219 | 2 |
| #9370 | 59 |