Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11728841 | C2 | semidirect |
| 4. #11728297 | C2 | semidirect |
| 5. #11725583 | C2 | semidirect |
| 7. #11725524 | C2 | semidirect |
| 297. C7 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3262 | 2 |
| #11728841 | 2 |
| #11728831 | 2 |
| #11728297 | 2 |
| #11725583 | 2 |
| #11725581 | 2 |
| #11725524 | 2 |
| #12169 | 7 |