Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
762 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21422663 | C2 | semidirect |
| 3. C2×#16837126 | C2 | semidirect |
| 4. #21421963 | C2 | semidirect |
| 5. C59×#2315 | C2 | semidirect |
| 9. #16837327 | C4 | semidirect |
| 11. #16837311 | C4 | semidirect |
| 21. C22×D236 | C2×C4 | semidirect |
| 30. C2×C4⋊Dic59 | C2×C4 | semidirect |
| 38. C59⋊#95 | C2×C4 | semidirect |
| 54. #95×C59 | D4 | semidirect |
| 205. #2315 | D59 | semidirect |
| 235. C59 | #9203 | semidirect |
| 269. #95 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429830 | 2 |
| #21422663 | 2 |
| C2×#16837126 | 2 |
| #21421963 | 2 |
| C59×#2315 | 2 |
| #9203 | 59 |