Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. C7×#1416 | C2 | semidirect |
| 4. #11725632 | C2 | semidirect |
| 6. #11725397 | C2 | semidirect |
| 7. #11725382 | C2 | semidirect |
| 42. #1416 | D7 | semidirect |
| 151. C7 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729258 | 2 |
| #11727079 | 2 |
| C7×#1416 | 2 |
| #11725632 | 2 |
| (C2×D7)⋊C32 | 2 |
| #11725397 | 2 |
| #11725382 | 2 |
| #13716 | 7 |