Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22577208 | C2 | semidirect |
| 8. C2×Dic548 | C4 | semidirect |
| 58. C137 | #2141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic548 | 2 |
| #22577441 | 2 |
| #22577208 | 2 |
| C2×M32×C137 | 2 |
| #2141 | 137 |