Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. C7×#550 | C2 | semidirect |
| 2. #90246 | C2 | semidirect |
| 3. #90010 | C2 | semidirect |
| 4. #90004 | C2 | semidirect |
| 5. #89844 | C2 | semidirect |
| 6. #89842 | C2 | semidirect |
| 7. #89811 | C2 | semidirect |
| 8. #89806 | C2 | semidirect |
| 9. C4×#1143 | C2 | semidirect |
| 10. #89792 | C2 | semidirect |
| 11. #89784 | C2 | semidirect |
| 78. #550 | D7 | semidirect |
| 93. C7×Q8 | #41 | semidirect |
| 216. Q8 | #1159 | semidirect |
| 243. C7 | #3332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#550 | 2 |
| #90246 | 2 |
| #90010 | 2 |
| #90004 | 2 |
| #89844 | 2 |
| #89842 | 2 |
| #89811 | 2 |
| #89806 | 2 |
| C4×#1143 | 2 |
| #89792 | 2 |
| #89784 | 2 |
| #3332 | 7 |