Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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. D7×#107 | C2 | semidirect |
| 3. C7×#357 | C2 | semidirect |
| 4. #89357 | C2 | semidirect |
| 5. (C2×D7)⋊C16 | C2 | semidirect |
| 6. #89299 | C2 | semidirect |
| 7. #89284 | C2 | semidirect |
| 42. #357 | D7 | semidirect |
| 122. C7 | #2232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89929 | 2 |
| D7×#107 | 2 |
| C7×#357 | 2 |
| #89357 | 2 |
| (C2×D7)⋊C16 | 2 |
| #89299 | 2 |
| #89284 | 2 |
| #2232 | 7 |