Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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. #21426405 | C2 | semidirect |
| 2. #21422311 | C2 | semidirect |
| 3. #21422308 | C2 | semidirect |
| 4. #21422307 | C2 | semidirect |
| 5. C2×C59×D32 | C2 | semidirect |
| 7. Dic944 | C22 | semidirect |
| 9. D1888 | C22 | semidirect |
| 10. C59⋊C64 | C22 | semidirect |
| 54. C2×D32 | D59 | semidirect |
| 71. C59 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426405 | 2 |
| #21422311 | 2 |
| #21422308 | 2 |
| #21422307 | 2 |
| C2×C59×D32 | 2 |
| #13742 | 59 |