Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. C7×#467 | C2 | semidirect |
| 3. C2×#6402 | C2 | semidirect |
| 4. C22⋊(C7⋊C16) | C2 | semidirect |
| 5. #89286 | C2 | semidirect |
| 7. C2×C7×Q16 | C22 | semidirect |
| 13. C7×#107 | C22 | semidirect |
| 16. C2×C7⋊C16 | C22 | semidirect |
| 38. #467 | D7 | semidirect |
| 60. C2×Q16 | C2×D7 | semidirect |
| 68. #107 | C2×D7 | semidirect |
| 72. C22×C7 | SD32 | semidirect |
| 124. C7 | #2187 | semidirect |
| 131. C22 | #6402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D56 | 2 |
| C7×#467 | 2 |
| C2×#6402 | 2 |
| C22⋊(C7⋊C16) | 2 |
| #89286 | 2 |
| #2187 | 7 |