Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11731088 | C2 | semidirect |
| 4. #11728521 | C2 | semidirect |
| 6. C7×#1303 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 20. #89621 | C4 | semidirect |
| 21. #89620 | C4 | semidirect |
| 78. #1303 | 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 |
|---|---|
| #11736512 | 2 |
| #11731088 | 2 |
| #11728544 | 2 |
| #11728521 | 2 |
| #11727223 | 2 |
| C7×#1303 | 2 |
| #11725519 | 2 |
| #9182 | 7 |