Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 1. C7×#500 | C2 | semidirect |
| 2. #89860 | C2 | semidirect |
| 3. #89857 | C2 | semidirect |
| 5. C8×C7⋊C8 | C2 | semidirect |
| 28. #500 | D7 | semidirect |
| 42. C7×C8 | SD16 | semidirect |
| 44. C7⋊C8 | D8 | semidirect |
| 89. C8 | #1143 | semidirect |
| 90. C7 | #1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#500 | 2 |
| #89860 | 2 |
| #89857 | 2 |
| #89467 | 2 |
| C8×C7⋊C8 | 2 |
| #1706 | 7 |