Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 149 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. C7×Q82 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 6. Q8×C7⋊C8 | C2 | semidirect |
| 7. #89792 | C2 | semidirect |
| 38. #1143 | Q8 | direct (N × H) |
| 44. Q82 | D7 | semidirect |
| 54. C7×Q8 | SD16 | semidirect |
| 55. C7×Q8 | C2×Q8 | semidirect |
| 67. C7⋊C8 | C2×Q8 | semidirect |
| 122. Q8 | #1143 | direct (N × H) |
| 123. Q8 | Q8×D7 | semidirect |
| 135. C7 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q82 | 2 |
| Q8×D28 | 2 |
| #89856 | 2 |
| #89851 | 2 |
| C4×#1143 | 2 |
| Q8×C7⋊C8 | 2 |
| #89792 | 2 |
| Q8×SD16 | 7 |