Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
570 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 270 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. Q8×#11758187 | C2 | semidirect |
| 2. #21462198 | C2 | semidirect |
| 3. #21462178 | C2 | semidirect |
| 4. D61⋊(C4⋊C16) | C2 | semidirect |
| 39. #11758226 | C16 | semidirect |
| 61. Q8×C61 | C2×C16 | semidirect |
| 68. D244 | C2×C16 | semidirect |
| 72. C4×D61 | C2×C16 | semidirect |
| 112. C61 | #33502 | semidirect |
| 155. Q8 | D61⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758187 | 2 |
| #21462198 | 2 |
| #21462178 | 2 |
| D61⋊(C4⋊C16) | 2 |
| C8×#11758226 | 2 |
| #33502 | 61 |