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 |
|---|---|---|
| 2. C2×C4×Dic14 | C2 | semidirect |
| 3. #89866 | C2 | semidirect |
| 4. #89847 | C2 | semidirect |
| 5. #89812 | C2 | semidirect |
| 6. #89806 | C2 | semidirect |
| 7. C4×#1142 | C2 | semidirect |
| 8. #89697 | C2 | semidirect |
| 84. C2×C4×C7 | SD16 | semidirect |
| 97. Dic14 | #41 | semidirect |
| 193. C2×C4 | #1142 | semidirect |
| 201. C7 | #3103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#532 | 2 |
| C2×C4×Dic14 | 2 |
| #89866 | 2 |
| #89847 | 2 |
| #89812 | 2 |
| #89806 | 2 |
| C4×#1142 | 2 |
| #89697 | 2 |
| #3103 | 7 |