Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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. #21460850 | C2 | semidirect |
| 3. #21460774 | C2 | semidirect |
| 4. C16×#92420 | C2 | semidirect |
| 45. C16×C61 | M16 | semidirect |
| 59. #92420 | D16 | semidirect |
| 93. C61 | #12081 | semidirect |
| 124. C16 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461451 | 2 |
| #21460850 | 2 |
| #21460774 | 2 |
| C16×#92420 | 2 |
| #21447665 | 2 |
| #12081 | 61 |