Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×C7×C22⋊C4 | C2 | semidirect |
| 3. C2×#6492 | C2 | semidirect |
| 4. #90019 | C2 | semidirect |
| 5. #89985 | C2 | semidirect |
| 6. #89731 | C2 | semidirect |
| 7. #89727 | C2 | semidirect |
| 8. #89718 | C2 | semidirect |
| 11. C23×C4×C7 | C22 | semidirect |
| 12. C23×C4×C7 | C22 | semidirect |
| 20. C2×C7×C22⋊C4 | C22 | semidirect |
| 22. C2×C22⋊Dic7 | C22 | semidirect |
| 23. C2×C22⋊Dic7 | C22 | semidirect |
| 25. C2×(C2×D7)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D7)⋊C4 | C22 | semidirect |
| 27. C2×Dic7⋊C4 | C22 | semidirect |
| 28. C7⋊#95 | C22 | semidirect |
| 69. C22×C22⋊C4 | D7 | semidirect |
| 123. C23×C4 | C2×D7 | semidirect |
| 124. C23×C4 | C2×D7 | semidirect |
| 134. C2×C22⋊C4 | C2×D7 | semidirect |
| 148. C22×C7 | #123 | semidirect |
| 249. C7 | #2405 | semidirect |
| 267. C22 | #6492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D7 | 2 |
| C22×C7×C22⋊C4 | 2 |
| C2×#6492 | 2 |
| #90019 | 2 |
| #89985 | 2 |
| #89731 | 2 |
| #89727 | 2 |
| #89718 | 2 |
| #2405 | 7 |