Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11727126 | C2 | semidirect |
| 3. C7×#1422 | C2 | semidirect |
| 4. #11725409 | C2 | semidirect |
| 5. C4×C7⋊C32 | C2 | semidirect |
| 33. #1422 | D7 | semidirect |
| 119. C7 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727126 | 2 |
| #11726810 | 2 |
| C7×#1422 | 2 |
| #11725409 | 2 |
| C4×C7⋊C32 | 2 |
| #13647 | 7 |