Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
618 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 128 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. #21460749 | C2 | direct (N × H) |
| 34. C22×Q8×C61 | C8 | semidirect |
| 49. C2×Q8×C61 | C2×C8 | semidirect |
| 142. C2×C61 | #1319 | semidirect |
| 156. C61 | C2×#1319 | semidirect |
| 162. C22×Q8 | #92420 | semidirect |
| 192. C2×Q8 | C2×#92420 | semidirect |
| 281. C2 | #21460749 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840607 | 2 |
| #21460749 | 2 |
| C2×#16839669 | 2 |
| C2×#1319 | 61 |