Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #89307 | C2 | direct (N × H) |
| 8. C7×M32 | C4 | semidirect |
| 10. C2×C7×C16 | C4 | semidirect |
| 13. #6386 | C4 | semidirect |
| 15. C2×C7⋊C16 | C4 | semidirect |
| 30. C7×C16 | C2×C4 | semidirect |
| 31. C7⋊C16 | C2×C4 | semidirect |
| 55. M32 | Dic7 | semidirect |
| 58. C2×C16 | Dic7 | semidirect |
| 84. C16 | C2×Dic7 | semidirect |
| 87. C2×C7 | #347 | semidirect |
| 103. C7 | C2×#347 | semidirect |
| 115. C2 | #89307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M32 | 2 |
| C2×#6389 | 2 |
| C2×#6386 | 2 |
| #89307 | 2 |
| C2×#347 | 7 |