Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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. #11741352 | C2 | semidirect |
| 3. C22×#6374 | C2 | semidirect |
| 4. #11736612 | C2 | semidirect |
| 5. C7×#2138 | C2 | semidirect |
| 6. #11729155 | C2 | semidirect |
| 7. #11728408 | C2 | semidirect |
| 8. #11726988 | C2 | semidirect |
| 9. #11726957 | C2 | semidirect |
| 19. #89953 | C22 | semidirect |
| 22. #89927 | C22 | semidirect |
| 31. C7×#358 | C22 | semidirect |
| 32. C7×#357 | C22 | semidirect |
| 33. Dic7⋊C16 | C22 | semidirect |
| 34. #89287 | C22 | semidirect |
| 86. #2138 | D7 | semidirect |
| 158. #358 | C2×D7 | semidirect |
| 159. #357 | C2×D7 | semidirect |
| 332. C7 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741352 | 2 |
| C2×#89965 | 2 |
| C22×#6374 | 2 |
| #11736612 | 2 |
| C7×#2138 | 2 |
| #11729155 | 2 |
| #11728408 | 2 |
| #11726988 | 2 |
| #11726957 | 2 |
| #33586 | 7 |