Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21448076 | C2 | semidirect |
| 2. #21448074 | C2 | semidirect |
| 3. #21448071 | C2 | semidirect |
| 5. #21445425 | C2 | semidirect |
| 6. C8×#11758185 | C2 | semidirect |
| 7. C61×#1709 | C2 | semidirect |
| 100. #1709 | D61 | semidirect |
| 119. C61 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448076 | 2 |
| #21448074 | 2 |
| #21448071 | 2 |
| #21448068 | 2 |
| #21445425 | 2 |
| C8×#11758185 | 2 |
| C61×#1709 | 2 |
| #12518 | 61 |