Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
874 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 874 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×#1749 | C2 | semidirect |
| 3. #11729283 | C2 | semidirect |
| 4. #11725285 | C2 | semidirect |
| 18. C7×#336 | C22 | semidirect |
| 19. #89319 | C22 | semidirect |
| 53. #1749 | D7 | semidirect |
| 121. #336 | C2×D7 | semidirect |
| 346. C7 | #7626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89711 | 2 |
| C7×#1749 | 2 |
| #11729283 | 2 |
| #11725285 | 2 |
| #7626 | 7 |