Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C7×C4⋊Q8 | C2 | semidirect |
| 3. #89999 | C2 | semidirect |
| 4. #89857 | C2 | semidirect |
| 5. #89855 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 7. #89697 | C2 | semidirect |
| 59. C2×C4⋊Q8 | D7 | semidirect |
| 73. C2×C4×C7 | SD16 | semidirect |
| 172. C2×C4 | #1143 | semidirect |
| 180. C7 | #3206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊Q8 | 2 |
| #90168 | 2 |
| #89999 | 2 |
| #89857 | 2 |
| #89855 | 2 |
| #89853 | 2 |
| #89697 | 2 |
| #3206 | 7 |