Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. C2×C8×Dic7 | C2 | semidirect |
| 5. #89757 | C2 | semidirect |
| 6. #89346 | C2 | semidirect |
| 7. #89324 | C2 | semidirect |
| 18. C7×#102 | C4 | semidirect |
| 106. #102 | Dic7 | semidirect |
| 205. C7 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#102 | 2 |
| #89993 | 2 |
| C2×#6406 | 2 |
| C2×C8×Dic7 | 2 |
| #89757 | 2 |
| #89346 | 2 |
| #89324 | 2 |
| #1934 | 7 |