Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11741225 | C2 | semidirect |
| 3. #11729830 | C2 | semidirect |
| 4. #11729766 | C2 | semidirect |
| 5. #11725527 | C2 | semidirect |
| 9. C7×#470 | C4 | semidirect |
| 10. C7×#469 | C4 | semidirect |
| 51. #6386 | D4 | semidirect |
| 102. #470 | Dic7 | semidirect |
| 103. #469 | Dic7 | semidirect |
| 256. C7 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3060 | 2 |
| #11741225 | 2 |
| #11729830 | 2 |
| #11729766 | 2 |
| #11725527 | 2 |
| #13077 | 7 |