Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×Dic14 | C2 | semidirect |
| 5. #89982 | C2 | semidirect |
| 6. #89748 | C2 | semidirect |
| 7. #89746 | C2 | semidirect |
| 8. #89716 | C2 | semidirect |
| 9. #89704 | C2 | semidirect |
| 19. #6499 | C4 | semidirect |
| 47. C2×Dic14 | C2×C4 | semidirect |
| 52. C22⋊Dic7 | C2×C4 | semidirect |
| 58. C4×Dic7 | C2×C4 | semidirect |
| 198. C7 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C2×#6499 | 2 |
| C2×C4×Dic14 | 2 |
| #89993 | 2 |
| #89982 | 2 |
| #89748 | 2 |
| #89746 | 2 |
| #89716 | 2 |
| #89704 | 2 |
| #2326 | 7 |