Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
170 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 75 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×#1398 | C2 | semidirect |
| 4. #11725405 | C2 | semidirect |
| 5. #11725325 | C2 | semidirect |
| 35. #1398 | D7 | semidirect |
| 129. C7 | #13642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726825 | 2 |
| C7×#1398 | 2 |
| #11725408 | 2 |
| #11725405 | 2 |
| #11725325 | 2 |
| #13642 | 7 |