Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 13. #16839580 | C4 | semidirect |
| 113. C61 | #12657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447574 | 2 |
| C2×#16839539 | 2 |
| #21445507 | 2 |
| #21443899 | 2 |
| C61×#1375 | 2 |
| #12657 | 61 |