Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
258 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 7. #16840684 | C4 | semidirect |
| 9. #16840603 | C4 | semidirect |
| 25. #14519713 | C8 | semidirect |
| 34. #107×C61 | C8 | semidirect |
| 113. C61 | #7182 | semidirect |
| 125. #107 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840684 | 2 |
| C2×#16840603 | 2 |
| #21445700 | 2 |
| #7182 | 61 |