Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #90413 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 6. #89627 | C2 | semidirect |
| 7. #89626 | C2 | semidirect |
| 8. #89623 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 59. #1142 | Q8 | semidirect |
| 105. Dic14 | SD16 | semidirect |
| 106. Dic14 | C2×Q8 | semidirect |
| 109. C7⋊C8 | C2×Q8 | semidirect |
| 215. C7 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90413 | 2 |
| D4×Dic14 | 2 |
| C7×#476 | 2 |
| #89851 | 2 |
| C4×#1142 | 2 |
| #89627 | 2 |
| #89626 | 2 |
| #89623 | 2 |
| #89602 | 2 |
| #89533 | 2 |
| #89530 | 2 |
| Q8×SD16 | 7 |