Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21447727 | C2 | semidirect |
| 3. #21443882 | C2 | semidirect |
| 4. #21443797 | C2 | semidirect |
| 6. C16×#92418 | C2 | semidirect |
| 65. C16×C61 | SD16 | semidirect |
| 88. #92418 | M32 | semidirect |
| 128. C61 | #12051 | semidirect |
| 173. C16 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447727 | 2 |
| C8×#11758200 | 2 |
| #21443882 | 2 |
| #21443797 | 2 |
| D4⋊#11758185 | 2 |
| C16×#92418 | 2 |
| C61×#2169 | 2 |
| #12051 | 61 |