Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11740572 | C2 | semidirect |
| 3. C7×#1521 | C2 | semidirect |
| 4. #11728515 | C2 | semidirect |
| 5. #11727318 | C2 | semidirect |
| 6. #11725553 | C2 | semidirect |
| 7. #11725439 | C2 | semidirect |
| 12. #89841 | C4 | semidirect |
| 13. #89839 | C4 | semidirect |
| 14. #89832 | C4 | semidirect |
| 15. #89830 | C4 | semidirect |
| 91. #1521 | D7 | semidirect |
| 381. C7 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740592 | 2 |
| #11740572 | 2 |
| C7×#1521 | 2 |
| #11728515 | 2 |
| #11727318 | 2 |
| #11725553 | 2 |
| #11725439 | 2 |
| #9370 | 7 |