Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21458957 | C2 | semidirect |
| 2. C2×#16839597 | C2 | semidirect |
| 3. #21447936 | C2 | semidirect |
| 4. #21444010 | C2 | semidirect |
| 5. #21444003 | C2 | semidirect |
| 6. #21443962 | C2 | semidirect |
| 7. C61×#2263 | C2 | semidirect |
| 17. C2×#14519683 | C22 | semidirect |
| 18. #16839592 | C22 | semidirect |
| 21. C2×D16×C61 | C22 | semidirect |
| 24. C61×M64 | C22 | semidirect |
| 117. #2263 | D61 | semidirect |
| 136. C2×D16 | C2×D61 | semidirect |
| 142. M64 | C2×D61 | semidirect |
| 146. C61 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458957 | 2 |
| C2×#16839597 | 2 |
| #21447936 | 2 |
| #21444010 | 2 |
| #21444003 | 2 |
| #21443962 | 2 |
| C61×#2263 | 2 |
| #13669 | 61 |