Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11729760 | C2 | semidirect |
| 3. C2×#89348 | C2 | semidirect |
| 4. #11727639 | C2 | semidirect |
| 5. #11727638 | C2 | semidirect |
| 50. #6386 | D4 | semidirect |
| 256. C7 | #13201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2930 | 2 |
| #11729760 | 2 |
| C2×#89348 | 2 |
| #11727639 | 2 |
| #11727638 | 2 |
| #13201 | 7 |