Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#131 | C2 | semidirect |
| 2. #90524 | C2 | semidirect |
| 3. C2×#6467 | C2 | semidirect |
| 4. #89906 | C2 | semidirect |
| 5. #89905 | C2 | semidirect |
| 6. #89888 | C2 | semidirect |
| 7. #89887 | C2 | semidirect |
| 8. C2×#6392 | C2 | semidirect |
| 49. C2×C7×C8 | D4 | semidirect |
| 62. C2×#131 | D7 | semidirect |
| 153. C2×C8 | C22⋊D7 | semidirect |
| 194. C7 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#131 | 2 |
| #90524 | 2 |
| C2×#6467 | 2 |
| #89906 | 2 |
| #89905 | 2 |
| #89888 | 2 |
| #89887 | 2 |
| C2×#6392 | 2 |
| #3061 | 7 |