Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 1. #11744364 | C2 | semidirect |
| 3. #11740362 | C2 | semidirect |
| 4. #11729899 | C2 | semidirect |
| 5. #11729468 | C2 | semidirect |
| 6. #11727798 | C2 | semidirect |
| 7. #11727794 | C2 | semidirect |
| 14. C22×#1136 | C22 | semidirect |
| 20. #89979 | C22 | semidirect |
| 23. #89771 | C22 | semidirect |
| 24. #89769 | C22 | semidirect |
| 25. #89328 | C22 | semidirect |
| 48. C2×#1136 | D4 | semidirect |
| 52. C22×C7⋊C8 | D4 | semidirect |
| 271. C7 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744364 | 2 |
| C7×#3025 | 2 |
| #11740362 | 2 |
| #11729899 | 2 |
| #11729468 | 2 |
| #11727798 | 2 |
| #11727794 | 2 |
| #21484 | 7 |