Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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×M32 | C2 | semidirect |
| 3. C22×C7⋊C16 | C2 | semidirect |
| 4. #89679 | C2 | direct (N × H) |
| 5. C2×#6372 | C2 | semidirect |
| 6. C2×D7×C16 | C2 | semidirect |
| 14. C7×M32 | C22 | semidirect |
| 18. C2×C7⋊C16 | C22 | semidirect |
| 19. #6372 | C22 | semidirect |
| 20. D7×C16 | C22 | semidirect |
| 44. C2×M32 | D7 | semidirect |
| 71. M32 | C2×D7 | semidirect |
| 106. C2×C7 | #504 | semidirect |
| 125. C7 | C2×#504 | semidirect |
| 137. C2 | #89679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6464 | 2 |
| C2×C7×M32 | 2 |
| C22×C7⋊C16 | 2 |
| #89679 | 2 |
| C2×#6372 | 2 |
| C2×D7×C16 | 2 |
| C2×#504 | 7 |