Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. C7×#364 | C2 | semidirect |
| 4. #89306 | C2 | semidirect |
| 5. #89258 | C2 | semidirect |
| 36. #364 | D7 | semidirect |
| 97. C7 | #2153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×M32 | 2 |
| #89461 | 2 |
| C7×#364 | 2 |
| #89306 | 2 |
| #89258 | 2 |
| #2153 | 7 |