Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
342 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C2×C7×#366 | C2 | semidirect |
| 4. #11725612 | C2 | semidirect |
| 5. #11725528 | C2 | semidirect |
| 35. C2×#366 | D7 | semidirect |
| 190. C7 | #13492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#366 | 2 |
| C2×(C2×D7)⋊C16 | 2 |
| #11728384 | 2 |
| #11725612 | 2 |
| #11725528 | 2 |
| #13492 | 7 |