Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 640 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 |
|---|---|---|
| 1. C7×#2889 | C2 | semidirect |
| 3. #11729898 | C2 | semidirect |
| 4. #11727903 | C2 | semidirect |
| 5. #11727900 | C2 | semidirect |
| 6. #11725507 | C2 | semidirect |
| 7. #11725506 | C2 | semidirect |
| 11. C2×#6512 | C4 | semidirect |
| 12. C22×#1143 | C4 | semidirect |
| 24. #90005 | C4 | semidirect |
| 28. #89997 | C4 | semidirect |
| 86. #2889 | D7 | semidirect |
| 460. C7 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2889 | 2 |
| #11741558 | 2 |
| #11729898 | 2 |
| #11727903 | 2 |
| #11727900 | 2 |
| #11725507 | 2 |
| #11725506 | 2 |
| #13098 | 7 |