Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
540 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 540 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. #21462740 | C2 | semidirect |
| 2. #21461940 | C2 | semidirect |
| 3. #21461118 | C2 | semidirect |
| 4. #21461112 | C2 | semidirect |
| 5. #21460665 | C2 | semidirect |
| 6. #21460652 | C2 | semidirect |
| 90. C2×D4×C61 | M16 | semidirect |
| 142. #11758194 | M16 | semidirect |
| 260. C61 | #8956 | semidirect |
| 325. C2×D4 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462740 | 2 |
| #21461940 | 2 |
| #21461118 | 2 |
| #21461112 | 2 |
| #21460665 | 2 |
| #21460652 | 2 |
| #21454623 | 2 |
| #8956 | 61 |