Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 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×Q82 | C2 | semidirect |
| 3. #89866 | C2 | semidirect |
| 4. #89865 | C2 | semidirect |
| 7. #89803 | C2 | semidirect |
| 8. #89802 | C2 | semidirect |
| 11. #89796 | C2 | semidirect |
| 74. Q82 | D7 | semidirect |
| 213. C7 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q82 | 2 |
| #90275 | 2 |
| #89866 | 2 |
| #89865 | 2 |
| #89861 | 2 |
| #89856 | 2 |
| #89803 | 2 |
| #89802 | 2 |
| #89800 | 2 |
| C4×#1143 | 2 |
| #89796 | 2 |
| #3369 | 7 |