Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 6. #89650 | C2 | semidirect |
| 7. #89646 | C2 | semidirect |
| 8. #89628 | C2 | semidirect |
| 32. C2×C7×C8 | Q8 | semidirect |
| 48. #1136 | Q8 | semidirect |
| 109. C2×C8 | Dic14 | semidirect |
| 144. C7 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90210 | 2 |
| C7×#427 | 2 |
| C2×#6392 | 2 |
| #89873 | 2 |
| #89767 | 2 |
| #89650 | 2 |
| #89646 | 2 |
| #89628 | 2 |
| #3164 | 7 |