Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
944 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#16839900 | C2 | semidirect |
| 2. C2×#16839496 | C2 | semidirect |
| 3. #21444089 | C2 | semidirect |
| 4. #21443662 | C2 | semidirect |
| 24. C22×Dic122 | D4 | semidirect |
| 32. C22⋊#92418 | D4 | semidirect |
| 69. C22×C4×C61 | SD16 | semidirect |
| 202. C61 | #9964 | semidirect |
| 269. C22×C4 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839900 | 2 |
| C2×#16839496 | 2 |
| #21444089 | 2 |
| #21443662 | 2 |
| C61×#2656 | 2 |
| #9964 | 61 |