Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 100 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. #21462626 | C2 | semidirect |
| 2. #21461116 | C2 | semidirect |
| 3. C2×#16840610 | C2 | semidirect |
| 4. #21461060 | C2 | semidirect |
| 5. #21460665 | C2 | semidirect |
| 6. #21460652 | C2 | semidirect |
| 99. C2×D244 | M16 | semidirect |
| 117. M16×C61 | M16 | semidirect |
| 258. C61 | #9097 | semidirect |
| 340. M16 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462626 | 2 |
| #21461116 | 2 |
| C2×#16840610 | 2 |
| #21461060 | 2 |
| #21460665 | 2 |
| #21460652 | 2 |
| #21454626 | 2 |
| #9097 | 61 |