Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 107. Dic14 | Q16 | semidirect |
| 214. C7 | #3395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90412 | 2 |
| #90258 | 2 |
| C7×#462 | 2 |
| #89954 | 2 |
| #89953 | 2 |
| #89864 | 2 |
| C4×#1144 | 2 |
| #89621 | 2 |
| #89602 | 2 |
| #89565 | 2 |
| #89562 | 2 |
| #3395 | 7 |