Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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 |
|---|---|---|
| 2. #90516 | C2 | semidirect |
| 3. C2×#6472 | C2 | semidirect |
| 4. C22×Dic28 | C2 | semidirect |
| 5. C7×#408 | C2 | semidirect |
| 6. #89892 | C2 | semidirect |
| 7. #89885 | C2 | semidirect |
| 8. #89511 | C2 | semidirect |
| 9. #89505 | C2 | semidirect |
| 92. #408 | D7 | semidirect |
| 260. C7 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6554 | 2 |
| #90516 | 2 |
| C2×#6472 | 2 |
| C22×Dic28 | 2 |
| C7×#408 | 2 |
| #89892 | 2 |
| #89885 | 2 |
| #89511 | 2 |
| #89505 | 2 |
| #3011 | 7 |