Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×C7×Q32 | C2 | semidirect |
| 4. #89360 | C2 | semidirect |
| 5. #89301 | C2 | semidirect |
| 32. C2×Q32 | D7 | semidirect |
| 95. C7 | #2222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Q32 | 2 |
| #89964 | 2 |
| #89673 | 2 |
| #89360 | 2 |
| #89301 | 2 |
| #2222 | 7 |