Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
208 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 208 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 |
|---|---|---|
| 6. C7×#382 | C4 | semidirect |
| 9. C7×#336 | C4 | semidirect |
| 53. #382 | Dic7 | semidirect |
| 55. #336 | Dic7 | semidirect |
| 171. C7 | #7412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2073 | 2 |
| #11725447 | 2 |
| #11725446 | 2 |
| #7412 | 7 |