Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
814 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊#1304 | C2 | semidirect |
| 5. C22×C7×C22⋊C4 | C4 | semidirect |
| 7. C7×#381 | C4 | semidirect |
| 56. C22×C22⋊C4 | Dic7 | semidirect |
| 59. #381 | Dic7 | semidirect |
| 178. C7 | #8746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2308 | 2 |
| #11729884 | 2 |
| C7⋊#1304 | 2 |
| #8746 | 7 |