Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2145 | C2 | semidirect |
| 3. #11729835 | C2 | semidirect |
| 4. #11729196 | C2 | semidirect |
| 5. #11728417 | C2 | semidirect |
| 6. #11728410 | C2 | semidirect |
| 7. #11725617 | C2 | semidirect |
| 67. C7×#106 | D4 | semidirect |
| 80. #2145 | D7 | semidirect |
| 240. #106 | C22⋊D7 | semidirect |
| 360. C7 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741349 | 2 |
| C7×#2145 | 2 |
| #11729835 | 2 |
| #11729196 | 2 |
| #11728417 | 2 |
| #11728410 | 2 |
| #11725617 | 2 |
| #13416 | 7 |