Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #11728533 | C2 | semidirect |
| 5. #11727582 | C2 | semidirect |
| 6. C7×#1275 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 21. #89466 | C4 | semidirect |
| 22. #89452 | C4 | semidirect |
| 73. #1275 | D7 | semidirect |
| 321. C7 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736714 | 2 |
| #11735936 | 2 |
| #11728544 | 2 |
| #11728533 | 2 |
| #11727582 | 2 |
| C7×#1275 | 2 |
| #11725544 | 2 |
| #9287 | 7 |