Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #21444018 | C2 | semidirect |
| 4. #21444000 | C2 | semidirect |
| 6. #21443953 | C2 | semidirect |
| 7. C4×Q32×C61 | C2 | semidirect |
| 10. #16839599 | C4 | semidirect |
| 27. #14519683 | C2×C4 | semidirect |
| 31. Q32×C61 | C2×C4 | semidirect |
| 83. C4×Q32 | D61 | semidirect |
| 105. C61 | #13652 | semidirect |
| 111. Q32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839599 | 2 |
| C4×D976 | 2 |
| #21444018 | 2 |
| #21444000 | 2 |
| #21443996 | 2 |
| #21443953 | 2 |
| C4×Q32×C61 | 2 |
| #13652 | 61 |