Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C2×C7×#101 | C2 | semidirect |
| 3. #89997 | C2 | semidirect |
| 6. #89891 | C2 | semidirect |
| 7. #89353 | C2 | semidirect |
| 59. C2×#101 | D7 | semidirect |
| 181. C7 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1143 | 2 |
| C2×C7×#101 | 2 |
| #89997 | 2 |
| #89903 | 2 |
| C2×#6397 | 2 |
| #89891 | 2 |
| #89353 | 2 |
| #2046 | 7 |