Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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×#557 | C2 | semidirect |
| 3. #89860 | C2 | semidirect |
| 4. #89859 | C2 | semidirect |
| 5. #89839 | C2 | semidirect |
| 6. #89838 | C2 | semidirect |
| 7. #89799 | C2 | semidirect |
| 8. #89799 | C2 | semidirect |
| 9. #89798 | C2 | semidirect |
| 10. C4×#1143 | C2 | semidirect |
| 11. #89796 | C2 | semidirect |
| 75. #557 | D7 | semidirect |
| 91. C7×Q8 | #41 | semidirect |
| 203. Q8 | #1161 | semidirect |
| 226. C7 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#557 | 2 |
| #90268 | 2 |
| #89860 | 2 |
| #89859 | 2 |
| #89839 | 2 |
| #89838 | 2 |
| #89799 | 2 |
| #89798 | 2 |
| C4×#1143 | 2 |
| #89796 | 2 |
| #3368 | 7 |