Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
194 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 83 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. C7×#1424 | C2 | semidirect |
| 5. #11725397 | C2 | semidirect |
| 6. #11725382 | C2 | semidirect |
| 7. #11725381 | C2 | semidirect |
| 19. #89242 | C4 | semidirect |
| 34. C7×C32 | C2×C4 | semidirect |
| 35. C7⋊C32 | C2×C4 | semidirect |
| 40. #1424 | D7 | semidirect |
| 98. C32 | C4×D7 | semidirect |
| 143. C7 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89242 | 2 |
| #11727079 | 2 |
| D7×#366 | 2 |
| C7×#1424 | 2 |
| #11725397 | 2 |
| #11725382 | 2 |
| #11725381 | 2 |
| #13634 | 7 |