Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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×C8×Q8 | C2 | semidirect |
| 2. #89799 | C2 | semidirect |
| 4. #89280 | C2 | semidirect |
| 5. #89253 | C2 | semidirect |
| 35. C8×Q8 | D7 | semidirect |
| 40. C7×Q8 | D8 | semidirect |
| 53. C7×C8 | SD16 | semidirect |
| 98. Q8 | D56 | semidirect |
| 112. C8 | #1143 | semidirect |
| 113. C7 | #1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×Q8 | 2 |
| #89799 | 2 |
| #89467 | 2 |
| #89280 | 2 |
| #89253 | 2 |
| #1668 | 7 |