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. #21448131 | C2 | semidirect |
| 3. C2×D1952 | C2 | semidirect |
| 4. #21447940 | C2 | semidirect |
| 5. #21444008 | C2 | semidirect |
| 6. #21443960 | C2 | semidirect |
| 7. C61×#1417 | C2 | semidirect |
| 13. C2×D976 | C22 | semidirect |
| 20. #16839596 | C22 | semidirect |
| 23. C2×C32×C61 | C22 | semidirect |
| 24. C61×#368 | C22 | semidirect |
| 121. #1417 | D61 | semidirect |
| 143. C2×C32 | C2×D61 | semidirect |
| 144. #368 | 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 |
| #21448131 | 2 |
| C2×D1952 | 2 |
| #21447940 | 2 |
| #21444008 | 2 |
| #21443960 | 2 |
| C61×#1417 | 2 |
| #13669 | 61 |