Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#6489 | C2 | semidirect |
| 4. #89759 | C2 | semidirect |
| 6. #89715 | C2 | semidirect |
| 7. C4×(C2×D7)⋊C4 | C2 | semidirect |
| 13. C22×C4×D7 | C4 | semidirect |
| 17. C2×C7×C4⋊C4 | C22 | semidirect |
| 19. C2×C42×C7 | C22 | semidirect |
| 23. C2×C4⋊Dic7 | C22 | semidirect |
| 24. C2×C4×Dic7 | C22 | semidirect |
| 25. C7⋊#95 | C22 | semidirect |
| 60. C2×#117 | D7 | semidirect |
| 81. C2×C4×C7 | C22⋊C4 | semidirect |
| 107. C2×C4⋊C4 | C2×D7 | semidirect |
| 112. C2×C42 | C2×D7 | semidirect |
| 127. C2×D7 | #117 | semidirect |
| 194. C2×C4 | (C2×D7)⋊C4 | semidirect |
| 201. C7 | #2280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D7 | 2 |
| C2×C7×#117 | 2 |
| C2×#6489 | 2 |
| #89759 | 2 |
| #89727 | 2 |
| #89715 | 2 |
| C4×(C2×D7)⋊C4 | 2 |
| #2280 | 7 |