Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#6481 | C2 | semidirect |
| 2. #90418 | C2 | semidirect |
| 4. C7×#462 | C2 | semidirect |
| 5. #89959 | C2 | semidirect |
| 6. #89857 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89610 | C2 | semidirect |
| 10. #89584 | C2 | semidirect |
| 11. #89578 | C2 | semidirect |
| 68. #1144 | D4 | semidirect |
| 88. #462 | D7 | semidirect |
| 167. C4×C7 | #137 | semidirect |
| 250. C7 | #3278 | semidirect |
| 265. C4 | #6481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6481 | 2 |
| #90418 | 2 |
| #90268 | 2 |
| C7×#462 | 2 |
| #89959 | 2 |
| #89857 | 2 |
| C4×#1144 | 2 |
| #89620 | 2 |
| #89610 | 2 |
| #89584 | 2 |
| #89578 | 2 |
| #3278 | 7 |