Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #11728567 | C2 | semidirect |
| 5. #11727610 | C2 | semidirect |
| 6. C7×#1291 | C2 | semidirect |
| 7. #11725557 | C2 | semidirect |
| 90. #1291 | D7 | semidirect |
| 360. C7 | #9312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736793 | 2 |
| #11735961 | 2 |
| #11728567 | 2 |
| #11728552 | 2 |
| #11727610 | 2 |
| C7×#1291 | 2 |
| #11725557 | 2 |
| #9312 | 7 |