Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#6472 | C2 | semidirect |
| 3. D4×Dic14 | C2 | semidirect |
| 4. C7×#436 | C2 | semidirect |
| 5. #89906 | C2 | semidirect |
| 6. #89621 | C2 | semidirect |
| 7. #89620 | C2 | semidirect |
| 8. #89510 | C2 | semidirect |
| 9. #89505 | C2 | semidirect |
| 10. C4×Dic28 | C2 | semidirect |
| 11. #89465 | C2 | semidirect |
| 79. Dic28 | D4 | semidirect |
| 93. #436 | D7 | semidirect |
| 165. C4×C7 | #137 | semidirect |
| 250. C7 | #3278 | semidirect |
| 265. C4 | #6472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6472 | 2 |
| #90244 | 2 |
| D4×Dic14 | 2 |
| C7×#436 | 2 |
| #89906 | 2 |
| #89621 | 2 |
| #89620 | 2 |
| #89510 | 2 |
| #89505 | 2 |
| C4×Dic28 | 2 |
| #89465 | 2 |
| #3278 | 7 |