Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
232 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 95 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. C16×Dic122 | C2 | semidirect |
| 4. #21443889 | C2 | semidirect |
| 5. #21443799 | C2 | semidirect |
| 7. C61×#1312 | C2 | semidirect |
| 60. #11758190 | C16 | semidirect |
| 80. Dic122 | C2×C16 | semidirect |
| 84. C8×C61 | C2×C16 | semidirect |
| 108. #1312 | D61 | semidirect |
| 128. C61 | SD16⋊C16 | semidirect |
| 192. C8 | C16×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic122 | 2 |
| C16×D244 | 2 |
| C8×#11758190 | 2 |
| #21443889 | 2 |
| #21443799 | 2 |
| #21443775 | 2 |
| C61×#1312 | 2 |
| SD16⋊C16 | 61 |