Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#6472 | C2 | semidirect |
| 3. C2×#6438 | C2 | semidirect |
| 4. C4×#1157 | C2 | semidirect |
| 5. C7×#423 | C2 | semidirect |
| 6. #89903 | C2 | semidirect |
| 7. #89892 | C2 | semidirect |
| 8. #89617 | C2 | semidirect |
| 9. #89616 | C2 | semidirect |
| 21. C2×Dic28 | C22 | semidirect |
| 24. C2×#1132 | C22 | semidirect |
| 28. C4×D28 | C22 | semidirect |
| 31. C4×Dic14 | C22 | semidirect |
| 32. C7×C4⋊C8 | C22 | semidirect |
| 34. #6390 | C22 | semidirect |
| 80. #423 | D7 | semidirect |
| 136. C4⋊C8 | C2×D7 | semidirect |
| 229. C7 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6472 | 2 |
| C2×#6471 | 2 |
| C2×#6438 | 2 |
| C4×#1157 | 2 |
| C7×#423 | 2 |
| #89903 | 2 |
| #89892 | 2 |
| #89617 | 2 |
| #89616 | 2 |
| #3040 | 7 |