Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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×#6514 | C2 | semidirect |
| 3. C2×#6472 | C2 | semidirect |
| 4. #90436 | C2 | semidirect |
| 5. C7×#413 | C2 | semidirect |
| 6. C2×#6398 | C2 | semidirect |
| 7. #89896 | C2 | semidirect |
| 8. #89527 | C2 | semidirect |
| 9. #89520 | C2 | semidirect |
| 20. C2×#1144 | C22 | semidirect |
| 22. C2×#1142 | C22 | semidirect |
| 33. C7×#101 | C22 | semidirect |
| 34. C7×#100 | C22 | semidirect |
| 35. #6398 | C22 | semidirect |
| 36. #6396 | C22 | semidirect |
| 91. #413 | D7 | semidirect |
| 156. #101 | C2×D7 | semidirect |
| 157. #100 | C2×D7 | semidirect |
| 263. C7 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6514 | 2 |
| #90513 | 2 |
| C2×#6472 | 2 |
| #90436 | 2 |
| C7×#413 | 2 |
| C2×#6398 | 2 |
| #89896 | 2 |
| #89527 | 2 |
| #89520 | 2 |
| #3069 | 7 |