Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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. #90516 | C2 | semidirect |
| 3. C2×#6514 | C2 | semidirect |
| 4. C22×#1142 | C2 | semidirect |
| 5. #90011 | C2 | semidirect |
| 6. #90006 | C2 | semidirect |
| 7. #90005 | C2 | semidirect |
| 8. #89990 | C2 | semidirect |
| 9. #89987 | C2 | semidirect |
| 20. C22×Dic14 | C22 | semidirect |
| 23. C2×#1144 | C22 | semidirect |
| 27. C2×#1142 | C22 | semidirect |
| 28. C2×#1142 | C22 | semidirect |
| 29. #6489 | C22 | semidirect |
| 30. #6487 | C22 | semidirect |
| 31. C2×#1136 | C22 | semidirect |
| 32. C22×C7⋊C8 | C22 | semidirect |
| 33. #6409 | C22 | semidirect |
| 34. #6406 | C22 | semidirect |
| 35. #6406 | C22 | semidirect |
| 36. C22⋊(C7⋊C8) | C22 | semidirect |
| 268. C7 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×H(5,𝔽2) | 2 |
| #90516 | 2 |
| C2×#6514 | 2 |
| C22×#1142 | 2 |
| #90011 | 2 |
| #90006 | 2 |
| #90005 | 2 |
| #89990 | 2 |
| #89987 | 2 |
| #3009 | 7 |