Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #21425041 | C2 | semidirect |
| 3. #21422608 | C2 | semidirect |
| 5. #21421988 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 24. C59×#474 | C4 | semidirect |
| 25. C59×#461 | C4 | semidirect |
| 192. #474 | Dic59 | semidirect |
| 193. #461 | Dic59 | semidirect |
| 210. C59 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426739 | 2 |
| #21425041 | 2 |
| #21422608 | 2 |
| #21422539 | 2 |
| #21421988 | 2 |
| #21421953 | 2 |
| C59×#3110 | 2 |
| #9327 | 59 |