Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21447721 | C2 | semidirect |
| 4. #21443888 | C2 | semidirect |
| 5. #21443799 | C2 | semidirect |
| 6. #21443738 | C2 | semidirect |
| 55. #11758200 | C16 | semidirect |
| 80. Dic122 | C2×C16 | semidirect |
| 88. #92418 | C2×C16 | semidirect |
| 128. C61 | SD16⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447721 | 2 |
| D4×#11758185 | 2 |
| C8×#11758200 | 2 |
| #21443888 | 2 |
| #21443799 | 2 |
| #21443738 | 2 |
| C61×D4⋊C16 | 2 |
| SD16⋊C16 | 61 |