Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. C8×Dic244 | C2 | semidirect |
| 3. #21443892 | C2 | semidirect |
| 4. #21443782 | C2 | semidirect |
| 6. #21443737 | C2 | semidirect |
| 64. Dic244 | M16 | semidirect |
| 85. C8×C61 | SD32 | semidirect |
| 128. C61 | #12071 | semidirect |
| 192. C8 | #14519721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519721 | 2 |
| C8×Dic244 | 2 |
| #21443892 | 2 |
| #21443782 | 2 |
| #21443780 | 2 |
| #21443737 | 2 |
| C61×#1589 | 2 |
| #12071 | 61 |