Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 4. #21422202 | C2 | semidirect |
| 5. #21422201 | C2 | semidirect |
| 6. #21422197 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 14. #16837437 | C4 | semidirect |
| 16. #106×D59 | C4 | semidirect |
| 152. #1384 | D59 | semidirect |
| 173. C59 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432688 | 2 |
| #21425716 | 2 |
| #21424139 | 2 |
| #21422202 | 2 |
| #21422201 | 2 |
| #21422197 | 2 |
| C59×#1384 | 2 |
| #12873 | 59 |