Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 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 |
|---|---|---|
| 2. #21447677 | C2 | semidirect |
| 4. #21443999 | C2 | semidirect |
| 6. C32×Dic61 | C2 | semidirect |
| 7. C61×#1424 | C2 | semidirect |
| 12. #16839601 | C4 | semidirect |
| 25. Dic488 | C2×C4 | semidirect |
| 36. C32×C61 | C2×C4 | semidirect |
| 81. Dic61 | SD64 | semidirect |
| 85. #1424 | D61 | semidirect |
| 105. C61 | C4×SD64 | semidirect |
| 122. C32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839601 | 2 |
| #21447677 | 2 |
| #21447665 | 2 |
| #21443999 | 2 |
| #21443996 | 2 |
| C32×Dic61 | 2 |
| C61×#1424 | 2 |
| C4×SD64 | 61 |