Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 5. C7×C4⋊Q8 | C4 | semidirect |
| 6. C7×#125 | C4 | semidirect |
| 30. C4×Dic7 | Q8 | semidirect |
| 51. C4⋊Q8 | Dic7 | semidirect |
| 52. #125 | Dic7 | semidirect |
| 103. C7 | #1994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| C42×Dic7 | 2 |
| #89696 | 2 |
| #89327 | 2 |
| #1994 | 7 |