Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21444595 | C2 | semidirect |
| 5. #21443688 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 7. C61×#1307 | C2 | semidirect |
| 120. #1307 | D61 | semidirect |
| 141. C61 | #10645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21444595 | 2 |
| #21444539 | 2 |
| #21444515 | 2 |
| #21444287 | 2 |
| #21443688 | 2 |
| #21443680 | 2 |
| C61×#1307 | 2 |
| #10645 | 61 |