Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
666 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 127 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. C7×#2112 | C2 | semidirect |
| 3. #11729717 | C2 | semidirect |
| 4. #11725328 | C2 | semidirect |
| 17. C7×C22⋊C16 | C22 | semidirect |
| 19. C22⋊(C7⋊C16) | C22 | semidirect |
| 53. #2112 | D7 | semidirect |
| 117. C22⋊C16 | C2×D7 | semidirect |
| 135. C22×D7 | M32 | semidirect |
| 317. C7 | #11418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D7)⋊C8 | 2 |
| C7×#2112 | 2 |
| #11729717 | 2 |
| #11725328 | 2 |
| #11418 | 7 |