Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 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. C7×#532 | C2 | semidirect |
| 2. C2×C4×D28 | C2 | semidirect |
| 3. #89856 | C2 | semidirect |
| 4. #89844 | C2 | semidirect |
| 5. #89808 | C2 | semidirect |
| 6. #89806 | C2 | semidirect |
| 7. #89786 | C2 | semidirect |
| 8. #89698 | C2 | semidirect |
| 12. C7×C4⋊Q8 | C22 | semidirect |
| 13. C7×#127 | C22 | semidirect |
| 18. C4×C7×D4 | C22 | semidirect |
| 27. #6406 | C22 | semidirect |
| 30. #6382 | C22 | semidirect |
| 31. C4⋊(C7⋊C8) | C22 | semidirect |
| 32. #6377 | C22 | semidirect |
| 66. #532 | D7 | semidirect |
| 100. D28 | #41 | semidirect |
| 108. C4⋊Q8 | C2×D7 | semidirect |
| 109. #127 | C2×D7 | semidirect |
| 118. C4×D4 | C2×D7 | semidirect |
| 215. C7 | #3109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#532 | 2 |
| C2×C4×D28 | 2 |
| #89856 | 2 |
| #89844 | 2 |
| #89808 | 2 |
| #89806 | 2 |
| #89786 | 2 |
| #89698 | 2 |
| #3109 | 7 |