Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×D16×D61 | C2 | semidirect |
| 2. C2×#16839597 | C2 | semidirect |
| 3. #21447902 | C2 | semidirect |
| 4. #21443998 | C2 | semidirect |
| 5. #21443997 | C2 | semidirect |
| 6. #21443956 | C2 | semidirect |
| 7. C2×C61×D32 | C2 | semidirect |
| 16. C2×#14519683 | C22 | semidirect |
| 17. #16839588 | C22 | semidirect |
| 20. C2×D16×C61 | C22 | semidirect |
| 22. C2×C32×C61 | C22 | semidirect |
| 31. D976 | D4 | semidirect |
| 44. D16×C61 | D4 | semidirect |
| 109. C2×D61 | D32 | semidirect |
| 116. C2×D32 | D61 | semidirect |
| 134. C2×D16 | C2×D61 | semidirect |
| 140. C2×C32 | C2×D61 | semidirect |
| 143. C61 | #13661 | semidirect |
| 159. D16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D61 | 2 |
| C2×#16839597 | 2 |
| #21447902 | 2 |
| #21443998 | 2 |
| #21443997 | 2 |
| #21443956 | 2 |
| C2×C61×D32 | 2 |
| #13661 | 61 |