Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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. C7×#1561 | C2 | semidirect |
| 3. #11729579 | C2 | semidirect |
| 6. #11728249 | C2 | semidirect |
| 7. #11725516 | C2 | semidirect |
| 68. #1561 | D7 | semidirect |
| 305. C7 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740800 | 2 |
| C7×#1561 | 2 |
| #11729579 | 2 |
| #11728275 | 2 |
| #11728256 | 2 |
| #11728249 | 2 |
| #11725516 | 2 |
| #10492 | 7 |