Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
150 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. #11725624 | C2 | semidirect |
| 3. #11725615 | C2 | semidirect |
| 4. C2×C7×D16 | C4 | semidirect |
| 8. C7×#367 | C4 | semidirect |
| 44. C2×D16 | Dic7 | semidirect |
| 49. #367 | Dic7 | semidirect |
| 123. C7 | #7422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2218 | 2 |
| #11725624 | 2 |
| #11725615 | 2 |
| #7422 | 7 |