Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #89863 | C2 | semidirect |
| 4. #89862 | C2 | semidirect |
| 6. #89803 | C2 | semidirect |
| 7. #89793 | C2 | semidirect |
| 81. C2×C4×C7 | Q16 | semidirect |
| 181. C2×C4 | #1144 | semidirect |
| 189. C7 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| #90161 | 2 |
| #89863 | 2 |
| #89862 | 2 |
| #89823 | 2 |
| #89803 | 2 |
| #89793 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| #3249 | 7 |