Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. C2×C4×Dic14 | C2 | semidirect |
| 5. #89790 | C2 | direct (N × H) |
| 6. C2×#6384 | C2 | semidirect |
| 7. C2×#6381 | C2 | semidirect |
| 8. C2×#6377 | C2 | semidirect |
| 17. C2×#1142 | C4 | semidirect |
| 25. C4×Dic14 | C22 | semidirect |
| 27. #6384 | C22 | semidirect |
| 28. #6381 | C22 | semidirect |
| 29. #6377 | C22 | semidirect |
| 46. C2×Dic14 | C2×C4 | semidirect |
| 53. #1142 | C2×C4 | semidirect |
| 59. C2×C7⋊C8 | C2×C4 | semidirect |
| 95. Dic14 | C22×C4 | semidirect |
| 97. C7⋊C8 | C22×C4 | semidirect |
| 167. C2×C7 | #440 | semidirect |
| 199. C7 | C2×#440 | semidirect |
| 217. C2 | #89790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C22×#1142 | 2 |
| C2×C4×Dic14 | 2 |
| C2×#6406 | 2 |
| #89790 | 2 |
| C2×#6384 | 2 |
| C2×#6381 | 2 |
| C2×#6377 | 2 |
| C2×#440 | 7 |