Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
226 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 24. Dic488 | C8 | semidirect |
| 56. #92420 | Q32 | semidirect |
| 87. C61 | C8×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461407 | 2 |
| #21460850 | 2 |
| #21460776 | 2 |
| C16×#92420 | 2 |
| #21447677 | 2 |
| C8×Q32 | 61 |