Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×C7×#127 | C2 | semidirect |
| 2. C2×#6495 | C2 | semidirect |
| 3. #90168 | C2 | semidirect |
| 4. #89848 | C2 | semidirect |
| 5. #89846 | C2 | semidirect |
| 6. #89845 | C2 | semidirect |
| 7. C4×#1136 | C2 | semidirect |
| 15. C2×#1142 | C22 | semidirect |
| 17. C2×#1141 | C22 | semidirect |
| 20. #6438 | C22 | semidirect |
| 21. #6437 | C22 | semidirect |
| 23. #6432 | C22 | semidirect |
| 24. #6377 | C22 | semidirect |
| 25. C4×C7⋊C8 | C22 | semidirect |
| 49. #1136 | D4 | semidirect |
| 53. C2×#127 | D7 | semidirect |
| 79. C7⋊C8 | C2×D4 | semidirect |
| 108. C4×C7 | AGL(1,ℤ/8) | semidirect |
| 162. C7 | #3151 | semidirect |
| 173. C4 | #6495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#127 | 2 |
| C2×#6495 | 2 |
| #90168 | 2 |
| #89848 | 2 |
| #89846 | 2 |
| #89845 | 2 |
| C4×#1136 | 2 |
| #3151 | 7 |