Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21426459 | C2 | semidirect |
| 5. #21422544 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 12. #16837698 | C4 | semidirect |
| 13. #16837603 | C4 | semidirect |
| 153. Dic118 | #104 | semidirect |
| 183. #1300 | D59 | semidirect |
| 212. C59 | #9326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434219 | 2 |
| #21426459 | 2 |
| #21425015 | 2 |
| #21422603 | 2 |
| #21422544 | 2 |
| #21421953 | 2 |
| C59×#1300 | 2 |
| #9326 | 59 |