Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1958 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1958 conjugacy classes of subgroups — too many to draw. Only its 587 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. #21454005 | C2 | direct (N × H) |
| 2. C2×C61⋊#401 | C2 | semidirect |
| 3. C2×#16839695 | C2 | semidirect |
| 11. C61⋊#401 | C22 | semidirect |
| 12. #16839695 | C22 | semidirect |
| 112. C2×C61 | #2834 | semidirect |
| 131. C61 | C2×#2834 | semidirect |
| 215. C2 | #21454005 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454005 | 2 |
| C2×C61⋊#401 | 2 |
| C2×#16839695 | 2 |
| C2×#16839687 | 2 |
| C2×#16839634 | 2 |
| C2×C61×#399 | 2 |
| C2×#2834 | 61 |