Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. C7×#477 | C2 | semidirect |
| 3. #89863 | C2 | semidirect |
| 5. Q8⋊(C7⋊C8) | C2 | semidirect |
| 7. #89279 | C2 | semidirect |
| 52. #477 | D7 | semidirect |
| 160. C7 | #1630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90276 | 2 |
| C7×#477 | 2 |
| #89863 | 2 |
| #89857 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| #89280 | 2 |
| #89279 | 2 |
| #1630 | 7 |