Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11725590 | C2 | semidirect |
| 4. C7×#533 | C4 | semidirect |
| 6. C7×#491 | C4 | semidirect |
| 10. C2×C7×#97 | C4 | semidirect |
| 64. #533 | Dic7 | semidirect |
| 66. #491 | Dic7 | semidirect |
| 71. C2×#97 | Dic7 | semidirect |
| 177. C7 | #13594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3135 | 2 |
| #11729573 | 2 |
| #11725590 | 2 |
| #13594 | 7 |