Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D976 | C2 | semidirect |
| 2. C2×#16839597 | C2 | direct (N × H) |
| 3. C22×#14519683 | C2 | semidirect |
| 4. C22×D16×C61 | C2 | semidirect |
| 7. C2×D976 | C22 | semidirect |
| 8. #16839597 | C22 | direct (N × H) |
| 9. C2×#14519683 | C22 | semidirect |
| 12. C2×D16×C61 | C22 | semidirect |
| 18. D976 | C23 | semidirect |
| 19. #14519683 | C23 | semidirect |
| 25. D16×C61 | C23 | semidirect |
| 59. C22×C61 | D32 | semidirect |
| 66. C22×D16 | D61 | semidirect |
| 70. C2×C61 | C2×D32 | semidirect |
| 78. C2×D16 | C2×D61 | semidirect |
| 82. C61 | C22×D32 | semidirect |
| 93. D16 | C22×D61 | semidirect |
| 129. C22 | #16839597 | direct (N × H) |
| 135. C2 | C2×#16839597 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D976 | 2 |
| C2×#16839597 | 2 |
| C22×#14519683 | 2 |
| C22×D16×C61 | 2 |
| C22×D32 | 61 |