Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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×#554 | C2 | semidirect |
| 2. #90276 | C2 | semidirect |
| 3. #89863 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. #89840 | C2 | semidirect |
| 6. #89838 | C2 | semidirect |
| 7. Q8×C7⋊C8 | C2 | semidirect |
| 8. C4×#1142 | C2 | semidirect |
| 9. #89788 | C2 | semidirect |
| 11. C4×#1141 | C2 | semidirect |
| 75. #554 | D7 | semidirect |
| 222. C7 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#554 | 2 |
| #90276 | 2 |
| #89863 | 2 |
| #89860 | 2 |
| #89840 | 2 |
| #89838 | 2 |
| Q8×C7⋊C8 | 2 |
| C4×#1142 | 2 |
| #89788 | 2 |
| #89787 | 2 |
| C4×#1141 | 2 |
| #3361 | 7 |