Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. C7×#487 | C2 | semidirect |
| 4. #89865 | C2 | semidirect |
| 5. #89853 | C2 | semidirect |
| 7. #89569 | C2 | semidirect |
| 9. #89453 | C2 | semidirect |
| 73. #487 | D7 | semidirect |
| 194. C7 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| D7×C4⋊Q8 | 2 |
| C7×#487 | 2 |
| #89865 | 2 |
| #89853 | 2 |
| #89574 | 2 |
| #89569 | 2 |
| C4×#1131 | 2 |
| #89453 | 2 |
| #3139 | 7 |