Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
732 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 2. #21461873 | C2 | semidirect |
| 3. #21461746 | C2 | semidirect |
| 4. #21461618 | C2 | semidirect |
| 6. C42×#92420 | C2 | semidirect |
| 67. C42×C61 | M16 | semidirect |
| 101. #92420 | #126 | semidirect |
| 144. C61 | #21666 | semidirect |
| 196. C42 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461891 | 2 |
| #21461873 | 2 |
| #21461746 | 2 |
| #21461618 | 2 |
| #21461560 | 2 |
| C42×#92420 | 2 |
| #21448367 | 2 |
| #21666 | 61 |