Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21447622 | C2 | semidirect |
| 3. #21443776 | C2 | semidirect |
| 4. C61×#2162 | C2 | semidirect |
| 15. #16839538 | C22 | semidirect |
| 17. C61×C4⋊C16 | C22 | semidirect |
| 123. #2162 | D61 | semidirect |
| 140. C4⋊C16 | C2×D61 | semidirect |
| 145. C61 | #11634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839841 | 2 |
| #21447622 | 2 |
| #21443776 | 2 |
| C61×#2162 | 2 |
| #11634 | 61 |