Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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×#99 | C2 | semidirect |
| 3. C2×#6407 | C2 | semidirect |
| 4. #89266 | C2 | direct (N × H) |
| 5. C24×D7 | C4 | semidirect |
| 9. C2×C22⋊Dic7 | C4 | semidirect |
| 12. #6500 | C4 | semidirect |
| 17. C7×#99 | C22 | semidirect |
| 19. #6407 | C22 | semidirect |
| 28. C23×D7 | C2×C4 | semidirect |
| 44. C22⋊Dic7 | C2×C4 | semidirect |
| 52. C2×#99 | D7 | semidirect |
| 106. #99 | C2×D7 | semidirect |
| 170. C2×C7 | AΣL(1,𝔽16) | semidirect |
| 211. C7 | C2×AΣL(1,𝔽16) | semidirect |
| 247. C2 | #89266 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6500 | 2 |
| C2×C7×#99 | 2 |
| C2×#6407 | 2 |
| #89266 | 2 |
| C2×AΣL(1,𝔽16) | 7 |