Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #11729856 | C2 | semidirect |
| 3. #11729855 | C2 | semidirect |
| 5. #11729538 | C2 | semidirect |
| 6. #11727625 | C2 | semidirect |
| 12. C7×#497 | C4 | semidirect |
| 13. C7×#494 | C4 | semidirect |
| 14. C7×#492 | C4 | semidirect |
| 100. #497 | Dic7 | semidirect |
| 101. #494 | Dic7 | semidirect |
| 102. #492 | Dic7 | semidirect |
| 238. C7 | #23360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3152 | 2 |
| #11729856 | 2 |
| #11729855 | 2 |
| #11729571 | 2 |
| #11729538 | 2 |
| #11727625 | 2 |
| #23360 | 7 |