Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 66 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. #21461451 | C2 | semidirect |
| 2. #21460852 | C2 | semidirect |
| 3. #21460774 | C2 | semidirect |
| 4. #21460730 | C2 | semidirect |
| 44. C16×C61 | M16 | semidirect |
| 90. C61 | #12086 | semidirect |
| 120. C16 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461451 | 2 |
| #21460852 | 2 |
| #21460774 | 2 |
| #21460730 | 2 |
| #21447665 | 2 |
| #12086 | 61 |