Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
528 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#16837440 | C2 | semidirect |
| 2. C2×#16837212 | C2 | semidirect |
| 3. #21425707 | C2 | semidirect |
| 4. #21422201 | C2 | semidirect |
| 16. C59×#467 | C4 | semidirect |
| 17. C59×#466 | C4 | semidirect |
| 31. #14273659 | D4 | semidirect |
| 168. #467 | Dic59 | semidirect |
| 169. #466 | Dic59 | semidirect |
| 178. C59 | #13002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837440 | 2 |
| C2×#16837212 | 2 |
| #21425707 | 2 |
| #21422201 | 2 |
| C59×#3050 | 2 |
| #13002 | 59 |