Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 103. Dic14 | Q16 | semidirect |
| 208. C7 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90413 | 2 |
| #90258 | 2 |
| C7×#477 | 2 |
| #89865 | 2 |
| C4×#1144 | 2 |
| #89647 | 2 |
| #89645 | 2 |
| #89621 | 2 |
| #89602 | 2 |
| #89565 | 2 |
| #89564 | 2 |
| #3363 | 7 |