Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 95 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×#1946 | C2 | semidirect |
| 3. #11728441 | C2 | semidirect |
| 4. #11728410 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 46. C7×#106 | D4 | semidirect |
| 55. #1946 | D7 | semidirect |
| 162. #106 | D28 | semidirect |
| 246. C7 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735944 | 2 |
| C7×#1946 | 2 |
| #11728441 | 2 |
| #11728410 | 2 |
| #11725469 | 2 |
| #13416 | 7 |