Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11728525 | C2 | semidirect |
| 5. #11727195 | C2 | semidirect |
| 6. #11725549 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 12. #89841 | C4 | semidirect |
| 13. #89837 | C4 | semidirect |
| 14. #89832 | C4 | semidirect |
| 15. #89827 | C4 | semidirect |
| 371. C7 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740581 | 2 |
| #11740578 | 2 |
| C7×#1500 | 2 |
| #11728525 | 2 |
| #11727195 | 2 |
| #11725549 | 2 |
| #11725421 | 2 |
| #8998 | 7 |