Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
226 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C7×#1372 | C2 | semidirect |
| 4. #11725307 | C2 | semidirect |
| 5. #11725275 | C2 | semidirect |
| 38. #1372 | D7 | semidirect |
| 159. C7 | #12024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D7×C16 | 2 |
| #11726324 | 2 |
| C7×#1372 | 2 |
| #11725307 | 2 |
| #11725275 | 2 |
| #12024 | 7 |