Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11728718 | C2 | semidirect |
| 4. #11728665 | C2 | semidirect |
| 6. #11725575 | C2 | semidirect |
| 7. #11725570 | C2 | semidirect |
| 266. C7 | #12391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3402 | 2 |
| #11729073 | 2 |
| #11728718 | 2 |
| #11728665 | 2 |
| #11725602 | 2 |
| #11725575 | 2 |
| #11725570 | 2 |
| #12391 | 7 |