Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 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. #21433158 | C2 | semidirect |
| 2. #21422652 | C2 | semidirect |
| 3. #21422625 | C2 | semidirect |
| 4. #21422456 | C2 | semidirect |
| 5. #21422005 | C2 | semidirect |
| 6. #21421972 | C2 | semidirect |
| 26. C59×#483 | C4 | semidirect |
| 28. C59×#480 | C4 | semidirect |
| 31. C59×#450 | C4 | semidirect |
| 33. C59×#447 | C4 | semidirect |
| 235. #483 | Dic59 | semidirect |
| 237. #480 | Dic59 | semidirect |
| 240. #450 | Dic59 | semidirect |
| 242. #447 | Dic59 | semidirect |
| 260. C59 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433158 | 2 |
| #21422652 | 2 |
| #21422625 | 2 |
| #21422456 | 2 |
| #21422005 | 2 |
| #21421972 | 2 |
| C59×#3194 | 2 |
| #9332 | 59 |