Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #11727120 | C2 | semidirect |
| 3. C7×#1397 | C2 | semidirect |
| 4. #11725401 | C2 | semidirect |
| 5. #11725316 | C2 | semidirect |
| 34. #1397 | D7 | semidirect |
| 117. C7 | #13648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727120 | 2 |
| #11726810 | 2 |
| C7×#1397 | 2 |
| #11725401 | 2 |
| #11725316 | 2 |
| #13648 | 7 |