Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#6408 | C2 | semidirect |
| 3. C2×#6407 | C2 | semidirect |
| 4. #89334 | C2 | semidirect |
| 5. #89331 | C2 | semidirect |
| 6. C22×C7×D4 | C4 | semidirect |
| 9. C7×#123 | C4 | semidirect |
| 14. C7×#120 | C4 | semidirect |
| 16. C2×C7×C22⋊C4 | C4 | semidirect |
| 25. C24×C7 | C2×C4 | semidirect |
| 40. C22×C4×C7 | C2×C4 | semidirect |
| 50. C7×C22⋊C4 | C2×C4 | semidirect |
| 51. C7×C22⋊C4 | C2×C4 | semidirect |
| 97. C22×D4 | Dic7 | semidirect |
| 101. #123 | Dic7 | semidirect |
| 106. #120 | Dic7 | semidirect |
| 109. C2×C22⋊C4 | Dic7 | semidirect |
| 141. C24 | C2×Dic7 | semidirect |
| 157. C22×C4 | C2×Dic7 | semidirect |
| 171. C22⋊C4 | C2×Dic7 | semidirect |
| 172. C22⋊C4 | C2×Dic7 | semidirect |
| 217. C7 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#534 | 2 |
| C2×#6408 | 2 |
| C2×#6407 | 2 |
| #89334 | 2 |
| #89331 | 2 |
| #2121 | 7 |