Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#16840686 | C2 | semidirect |
| 4. #21460884 | C2 | semidirect |
| 15. C2×#14519716 | C4 | semidirect |
| 16. C2×#14519716 | C4 | semidirect |
| 19. C22×#11758185 | C4 | semidirect |
| 20. C22×C16×C61 | C4 | semidirect |
| 80. C16×C61 | C22⋊C4 | semidirect |
| 82. #11758185 | C22⋊C4 | semidirect |
| 114. C22×C61 | #365 | semidirect |
| 147. C22×C16 | #6923 | semidirect |
| 155. C61 | #12831 | semidirect |
| 217. C16 | C22⋊#6923 | semidirect |
| 255. C22 | #16840686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840686 | 2 |
| #21461698 | 2 |
| #21461695 | 2 |
| #21460884 | 2 |
| C22×#14519716 | 2 |
| #12831 | 61 |