Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4×Q8×D7 | C2 | semidirect |
| 3. C7×#477 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89799 | C2 | semidirect |
| 6. #89661 | C2 | semidirect |
| 7. #89654 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89607 | C2 | semidirect |
| 10. #89589 | C2 | semidirect |
| 11. #89578 | C2 | semidirect |
| 88. #477 | D7 | semidirect |
| 99. C7×Q8 | #41 | semidirect |
| 125. Dic14 | #41 | semidirect |
| 230. Q8 | #1161 | semidirect |
| 256. C7 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90416 | 2 |
| C4×Q8×D7 | 2 |
| C7×#477 | 2 |
| #89863 | 2 |
| #89799 | 2 |
| #89661 | 2 |
| #89654 | 2 |
| #89620 | 2 |
| #89607 | 2 |
| #89589 | 2 |
| #89578 | 2 |
| #3112 | 7 |