Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. #21446809 | C2 | semidirect |
| 3. #21444575 | C2 | semidirect |
| 4. #21444500 | C2 | semidirect |
| 6. C8×#11758194 | C2 | semidirect |
| 95. #11758194 | SD16 | semidirect |
| 127. C8×C61 | #100 | semidirect |
| 179. C61 | #9793 | semidirect |
| 285. C8 | #14519694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446809 | 2 |
| #21446660 | 2 |
| #21444575 | 2 |
| #21444500 | 2 |
| #21444487 | 2 |
| C8×#11758194 | 2 |
| C2×C61×#492 | 2 |
| #9793 | 61 |