Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. Q16×Dic7 | C2 | semidirect |
| 4. #89953 | C2 | semidirect |
| 8. #89646 | C2 | semidirect |
| 9. #89645 | C2 | semidirect |
| 10. #89564 | C2 | semidirect |
| 11. #89562 | C2 | semidirect |
| 95. C2×Dic7 | Q16 | semidirect |
| 209. C7 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90313 | 2 |
| C7×#467 | 2 |
| Q16×Dic7 | 2 |
| #89953 | 2 |
| #89888 | 2 |
| C2×C8×Dic7 | 2 |
| #89823 | 2 |
| #89646 | 2 |
| #89645 | 2 |
| #89564 | 2 |
| #89562 | 2 |
| #3170 | 7 |