Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #11725382 | C2 | semidirect |
| 5. #11725381 | C2 | semidirect |
| 14. #89294 | C4 | semidirect |
| 29. C7⋊C32 | C2×C4 | semidirect |
| 126. C7 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2158 | 2 |
| C2×#89299 | 2 |
| C2×#89294 | 2 |
| #11725382 | 2 |
| #11725381 | 2 |
| #13634 | 7 |