Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11726836 | C2 | semidirect |
| 4. C7×#1398 | C2 | semidirect |
| 6. #11725411 | C2 | semidirect |
| 7. #11725407 | C2 | semidirect |
| 19. Dic112 | C4 | semidirect |
| 20. #89244 | C4 | semidirect |
| 46. #1398 | D7 | semidirect |
| 155. C7 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727128 | 2 |
| #11726839 | 2 |
| #11726836 | 2 |
| C7×#1398 | 2 |
| #11725412 | 2 |
| #11725411 | 2 |
| #11725407 | 2 |
| #13657 | 7 |