Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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×#1980 | C2 | semidirect |
| 3. #11729565 | C2 | semidirect |
| 4. #11727621 | C2 | semidirect |
| 5. #11727601 | C2 | semidirect |
| 6. C4×#6382 | C2 | semidirect |
| 7. #11727223 | C2 | semidirect |
| 14. #89860 | C4 | semidirect |
| 15. #89850 | C4 | semidirect |
| 16. #89845 | C4 | semidirect |
| 17. #89842 | C4 | semidirect |
| 80. #1980 | D7 | semidirect |
| 202. C7⋊C8 | #104 | semidirect |
| 373. C7 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740736 | 2 |
| C7×#1980 | 2 |
| #11729565 | 2 |
| #11727621 | 2 |
| #11727601 | 2 |
| C4×#6382 | 2 |
| #11727223 | 2 |
| #9721 | 7 |