Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #11729158 | C2 | semidirect |
| 3. C7×C22⋊C32 | C2 | semidirect |
| 4. #11725402 | C2 | semidirect |
| 5. #11725402 | C2 | semidirect |
| 6. #11725398 | C2 | semidirect |
| 7. #11725397 | C2 | semidirect |
| 43. C22⋊C32 | D7 | semidirect |
| 156. C7 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729167 | 2 |
| #11729158 | 2 |
| C7×C22⋊C32 | 2 |
| #11725402 | 2 |
| #11725398 | 2 |
| #11725397 | 2 |
| #13713 | 7 |