Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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 |
| 3. Q8×D28 | C2 | semidirect |
| 4. C7×#462 | C2 | semidirect |
| 5. #89958 | C2 | semidirect |
| 6. #89864 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. #89613 | C2 | semidirect |
| 9. #89610 | C2 | semidirect |
| 10. #89588 | C2 | semidirect |
| 11. #89582 | C2 | semidirect |
| 68. #1143 | D4 | semidirect |
| 88. #462 | D7 | semidirect |
| 165. C4×C7 | #137 | semidirect |
| 246. C7 | #3276 | semidirect |
| 261. 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 |
| #90417 | 2 |
| Q8×D28 | 2 |
| C7×#462 | 2 |
| #89958 | 2 |
| #89864 | 2 |
| C4×#1143 | 2 |
| #89613 | 2 |
| #89610 | 2 |
| #89588 | 2 |
| #89582 | 2 |
| #3276 | 7 |