Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
176 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 55 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. #11725398 | C2 | semidirect |
| 7. #11725382 | C2 | semidirect |
| 42. #1416 | D7 | semidirect |
| 153. C7 | #13714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729258 | 2 |
| D7×#366 | 2 |
| C7×#1416 | 2 |
| #11725632 | 2 |
| (C2×D7)⋊C32 | 2 |
| #11725398 | 2 |
| #11725382 | 2 |
| #13714 | 7 |