Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 2. C22×#6401 | C2 | semidirect |
| 3. C2×#89681 | C2 | semidirect |
| 4. #11736614 | C2 | semidirect |
| 5. C7×#2140 | C2 | semidirect |
| 6. #11729175 | C2 | semidirect |
| 7. #11728405 | C2 | semidirect |
| 8. #11726959 | C2 | semidirect |
| 9. #11726958 | C2 | semidirect |
| 27. C2×Dic56 | C22 | semidirect |
| 28. C2×#6374 | C22 | semidirect |
| 29. #89645 | C22 | semidirect |
| 32. Dic7⋊C16 | C22 | semidirect |
| 33. #89287 | C22 | semidirect |
| 34. #89286 | C22 | semidirect |
| 56. C2×Dic28 | D4 | semidirect |
| 85. #2140 | D7 | semidirect |
| 332. C7 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741275 | 2 |
| C22×#6401 | 2 |
| C2×#89681 | 2 |
| #11736614 | 2 |
| C7×#2140 | 2 |
| #11729175 | 2 |
| #11728405 | 2 |
| #11726959 | 2 |
| #11726958 | 2 |
| #33587 | 7 |