Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #11729768 | C2 | semidirect |
| 3. #11729765 | C2 | semidirect |
| 4. #11729616 | C2 | semidirect |
| 5. #11729613 | C2 | semidirect |
| 6. C22×C7×D8 | C4 | semidirect |
| 13. C7×#427 | C4 | semidirect |
| 14. C7×#418 | C4 | semidirect |
| 114. C22×D8 | Dic7 | semidirect |
| 122. #427 | Dic7 | semidirect |
| 123. #418 | Dic7 | semidirect |
| 308. C7 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3058 | 2 |
| #11729768 | 2 |
| #11729765 | 2 |
| #11729616 | 2 |
| #11729613 | 2 |
| #13234 | 7 |