Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
980 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#89983 | C2 | semidirect |
| 3. #11729880 | C2 | semidirect |
| 4. C2×#89332 | C2 | semidirect |
| 5. #11725430 | C2 | semidirect |
| 7. C2×C7×#121 | C4 | semidirect |
| 13. C7×#380 | C4 | semidirect |
| 51. C7⋊#95 | D4 | semidirect |
| 112. C2×#121 | Dic7 | semidirect |
| 121. #380 | Dic7 | semidirect |
| 364. C7 | #9158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2847 | 2 |
| C2×#89983 | 2 |
| #11729880 | 2 |
| C2×#89332 | 2 |
| #11725430 | 2 |
| #9158 | 7 |