Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11739908 | C2 | semidirect |
| 3. C7×#1479 | C2 | semidirect |
| 6. #11725552 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 14. #89803 | C4 | semidirect |
| 16. #89799 | C4 | semidirect |
| 77. #1479 | D7 | semidirect |
| 366. C7 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739908 | 2 |
| #11739886 | 2 |
| C7×#1479 | 2 |
| #11728544 | 2 |
| #11728543 | 2 |
| #11725552 | 2 |
| #11725544 | 2 |
| #9182 | 7 |