Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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×#117 | C2 | semidirect |
| 3. C23×C7⋊C8 | C2 | semidirect |
| 4. #89774 | C2 | direct (N × H) |
| 5. C2×#6384 | C2 | semidirect |
| 6. C2×#6383 | C2 | semidirect |
| 11. C2×#1157 | C4 | semidirect |
| 17. C7×#117 | C22 | semidirect |
| 23. C22×C7⋊C8 | C22 | semidirect |
| 24. #6384 | C22 | semidirect |
| 25. #6383 | C22 | semidirect |
| 41. #1157 | C2×C4 | semidirect |
| 61. C2×#117 | D7 | semidirect |
| 107. #117 | C2×D7 | semidirect |
| 161. C2×C7 | #416 | semidirect |
| 194. C7 | C2×#416 | semidirect |
| 212. C2 | #89774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1157 | 2 |
| C2×C7×#117 | 2 |
| C23×C7⋊C8 | 2 |
| #89774 | 2 |
| C2×#6384 | 2 |
| C2×#6383 | 2 |
| C2×#416 | 7 |