Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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×C7×#104 | C2 | semidirect |
| 3. #90004 | C2 | semidirect |
| 4. C2×#6397 | C2 | semidirect |
| 5. #89893 | C2 | semidirect |
| 6. #89711 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 49. C7×M16 | D4 | semidirect |
| 67. C2×#104 | D7 | semidirect |
| 173. M16 | C22⋊D7 | semidirect |
| 231. C7 | #2037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90521 | 2 |
| C2×C7×#104 | 2 |
| #90004 | 2 |
| C2×#6397 | 2 |
| #89893 | 2 |
| #89711 | 2 |
| #89318 | 2 |
| #2037 | 7 |