Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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×#541 | C2 | semidirect |
| 3. #89855 | C2 | semidirect |
| 4. #89838 | C2 | semidirect |
| 6. #89817 | C2 | semidirect |
| 7. #89798 | C2 | semidirect |
| 8. C4×#1143 | C2 | semidirect |
| 9. #89772 | C2 | semidirect |
| 11. C7×C4⋊Q8 | C22 | semidirect |
| 14. C7×#125 | C22 | semidirect |
| 16. C4×C7×Q8 | C22 | semidirect |
| 25. #6409 | C22 | semidirect |
| 26. #6409 | C22 | semidirect |
| 30. #6382 | C22 | semidirect |
| 31. #6381 | C22 | semidirect |
| 32. C4⋊(C7⋊C8) | C22 | semidirect |
| 33. #6377 | C22 | semidirect |
| 34. C4×C7⋊C8 | C22 | semidirect |
| 64. #541 | D7 | semidirect |
| 97. C4⋊Q8 | C2×D7 | semidirect |
| 100. #125 | C2×D7 | semidirect |
| 102. C4×Q8 | C2×D7 | semidirect |
| 186. C7 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#541 | 2 |
| #90212 | 2 |
| #89855 | 2 |
| #89838 | 2 |
| #89818 | 2 |
| #89817 | 2 |
| #89798 | 2 |
| C4×#1143 | 2 |
| #89772 | 2 |
| #3123 | 7 |