Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21457135 | C2 | semidirect |
| 2. #21456760 | C2 | semidirect |
| 3. #21446763 | C2 | semidirect |
| 4. #21446747 | C2 | semidirect |
| 5. #21444314 | C2 | semidirect |
| 6. #21443670 | C2 | semidirect |
| 107. M16×C61 | SD16 | semidirect |
| 240. C61 | #10194 | semidirect |
| 319. M16 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457135 | 2 |
| #21456760 | 2 |
| #21446763 | 2 |
| #21446747 | 2 |
| #21444314 | 2 |
| #21443670 | 2 |
| C61×#3151 | 2 |
| #10194 | 61 |