Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 10. #89261 | C4 | direct (N × H) |
| 11. #89256 | C4 | semidirect |
| 12. C4×C7⋊C16 | C4 | semidirect |
| 46. C7⋊C16 | C42 | semidirect |
| 87. C4×C7 | #347 | semidirect |
| 124. C7 | C4×#347 | semidirect |
| 130. C4 | #89261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#97 | 2 |
| C2×#89261 | 2 |
| C4×#6386 | 2 |
| C4×#347 | 7 |