Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#16837218 | C2 | semidirect |
| 5. #21422194 | C2 | semidirect |
| 6. #21422176 | C2 | semidirect |
| 7. C59×#1971 | C2 | semidirect |
| 12. C2×#14273673 | C4 | semidirect |
| 13. C2×#14273670 | C4 | semidirect |
| 169. #1971 | D59 | semidirect |
| 196. C59 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| C2×#16837525 | 2 |
| C2×#16837218 | 2 |
| C2×#16837211 | 2 |
| #21422194 | 2 |
| #21422176 | 2 |
| C59×#1971 | 2 |
| #13039 | 59 |