Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C7×#519 | C2 | semidirect |
| 2. C2×#6505 | C2 | semidirect |
| 3. C22×#1143 | C2 | semidirect |
| 5. #89800 | C2 | semidirect |
| 6. #89799 | C2 | semidirect |
| 7. #89774 | C2 | semidirect |
| 8. #89773 | C2 | semidirect |
| 9. #89771 | C2 | semidirect |
| 14. C4×C7×Q8 | C22 | semidirect |
| 18. C2×#1144 | C22 | semidirect |
| 22. C2×#1143 | C22 | semidirect |
| 29. #6384 | C22 | semidirect |
| 31. #6383 | C22 | semidirect |
| 32. C4⋊(C7⋊C8) | C22 | semidirect |
| 37. C2×C7×Q8 | D4 | semidirect |
| 71. #519 | D7 | semidirect |
| 121. C4×Q8 | C2×D7 | semidirect |
| 150. C2×Q8 | D28 | semidirect |
| 212. C7 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#519 | 2 |
| C2×#6505 | 2 |
| C22×#1143 | 2 |
| #90216 | 2 |
| #89800 | 2 |
| #89799 | 2 |
| #89774 | 2 |
| #89773 | 2 |
| #89771 | 2 |
| #3043 | 7 |