Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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. #89968 | C2 | semidirect |
| 3. #89362 | C2 | semidirect |
| 4. #89301 | C2 | semidirect |
| 5. C16×Dic7 | C2 | semidirect |
| 8. C7×Q32 | C4 | semidirect |
| 9. C7×SD32 | C4 | semidirect |
| 10. C7×D16 | C4 | semidirect |
| 48. Q32 | Dic7 | semidirect |
| 49. SD32 | Dic7 | semidirect |
| 50. D16 | Dic7 | semidirect |
| 89. C7 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#508 | 2 |
| #89968 | 2 |
| #89362 | 2 |
| #89301 | 2 |
| C16×Dic7 | 2 |
| #2178 | 7 |