Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 2. #90261 | C2 | semidirect |
| 3. C7×#460 | C2 | semidirect |
| 4. #89936 | C2 | semidirect |
| 5. #89935 | C2 | semidirect |
| 6. #89842 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. #89618 | C2 | semidirect |
| 9. #89603 | C2 | semidirect |
| 10. #89538 | C2 | semidirect |
| 11. #89536 | C2 | semidirect |
| 82. #460 | D7 | semidirect |
| 89. C7×Q8 | #41 | semidirect |
| 203. Q8 | #1159 | semidirect |
| 226. C7 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90409 | 2 |
| #90261 | 2 |
| C7×#460 | 2 |
| #89936 | 2 |
| #89935 | 2 |
| #89842 | 2 |
| C4×#1143 | 2 |
| #89618 | 2 |
| #89603 | 2 |
| #89538 | 2 |
| #89536 | 2 |
| #3368 | 7 |