Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
164 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11725325 | C2 | semidirect |
| 4. #11725316 | C2 | semidirect |
| 121. C7 | #13643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2108 | 2 |
| #11725615 | 2 |
| #11725325 | 2 |
| #11725316 | 2 |
| #13643 | 7 |