Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11728360 | C2 | semidirect |
| 5. C7×#1387 | C2 | semidirect |
| 6. #11725616 | C2 | semidirect |
| 7. #11725538 | C2 | semidirect |
| 61. #1387 | D7 | semidirect |
| 270. C7 | #13484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729193 | 2 |
| #11728450 | 2 |
| #11728360 | 2 |
| #11728352 | 2 |
| C7×#1387 | 2 |
| #11725616 | 2 |
| #11725538 | 2 |
| #13484 | 7 |