Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#16839587 | C2 | semidirect |
| 4. #21443911 | C2 | semidirect |
| 5. C61×#1380 | C2 | semidirect |
| 9. C2×C16×D61 | C4 | semidirect |
| 60. #11758185 | C22⋊C4 | semidirect |
| 96. C2×D61 | #366 | semidirect |
| 107. #1380 | D61 | semidirect |
| 124. C61 | #12834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D61 | 2 |
| C2×#16839587 | 2 |
| #21445845 | 2 |
| #21443911 | 2 |
| C61×#1380 | 2 |
| #12834 | 61 |