Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1354 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 368 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. #21461557 | C2 | semidirect |
| 3. #21461545 | C2 | semidirect |
| 7. D61⋊(C22⋊C8) | C4 | semidirect |
| 9. C2×#14519832 | C22 | semidirect |
| 10. #16840628 | C22 | semidirect |
| 19. C2×D61⋊C8 | C2×C4 | semidirect |
| 21. #14519834 | C2×C4 | semidirect |
| 87. C22×D61 | #97 | semidirect |
| 156. C61 | #20526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊(C22⋊C8) | 2 |
| #21461557 | 2 |
| #21461545 | 2 |
| C2×#16839609 | 2 |
| #20526 | 61 |