Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. #11741275 | C2 | semidirect |
| 2. C22×#6400 | C2 | semidirect |
| 3. C2×#89680 | C2 | semidirect |
| 4. #11736612 | C2 | semidirect |
| 5. C7×#2140 | C2 | semidirect |
| 6. #11729175 | C2 | semidirect |
| 7. #11728405 | C2 | semidirect |
| 8. #11726957 | C2 | semidirect |
| 9. #11726956 | C2 | semidirect |
| 18. #89927 | C22 | semidirect |
| 20. #89923 | C22 | semidirect |
| 27. C2×#6374 | C22 | semidirect |
| 28. C2×D112 | C22 | semidirect |
| 29. #89644 | C22 | semidirect |
| 31. C7×#357 | C22 | semidirect |
| 32. Dic7⋊C16 | C22 | semidirect |
| 33. #89287 | C22 | semidirect |
| 34. #89286 | C22 | semidirect |
| 59. C2×D56 | D4 | semidirect |
| 85. #2140 | D7 | semidirect |
| 159. #357 | C2×D7 | semidirect |
| 339. C7 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741275 | 2 |
| C22×#6400 | 2 |
| C2×#89680 | 2 |
| #11736612 | 2 |
| C7×#2140 | 2 |
| #11729175 | 2 |
| #11728405 | 2 |
| #11726957 | 2 |
| #11726956 | 2 |
| #33585 | 7 |