Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 19. #6389 | C4 | semidirect |
| 71. C7×C8 | C4⋊C4 | semidirect |
| 72. C7⋊C8 | C4⋊C4 | semidirect |
| 148. C8 | Dic7⋊C4 | semidirect |
| 149. C7 | #1847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#106 | 2 |
| C2×#6392 | 2 |
| C2×#6389 | 2 |
| #89749 | 2 |
| #89748 | 2 |
| C2×#6382 | 2 |
| C2×#6381 | 2 |
| #1847 | 7 |