Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21447704 | C2 | semidirect |
| 3. #21447694 | C2 | semidirect |
| 4. #21444008 | C2 | semidirect |
| 5. #21444005 | C2 | semidirect |
| 6. #21443954 | C2 | semidirect |
| 7. C61×#1426 | C2 | semidirect |
| 12. #16839601 | C4 | semidirect |
| 13. D1952 | C4 | semidirect |
| 25. Dic488 | C2×C4 | semidirect |
| 29. D976 | C2×C4 | semidirect |
| 38. C32×C61 | C2×C4 | semidirect |
| 87. #1426 | D61 | semidirect |
| 108. C61 | #13658 | semidirect |
| 126. C32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448134 | 2 |
| #21447704 | 2 |
| #21447694 | 2 |
| #21444008 | 2 |
| #21444005 | 2 |
| #21443954 | 2 |
| C61×#1426 | 2 |
| #13658 | 61 |