Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×D84 | C2 | semidirect |
| 2. C3×#6493 | C2 | semidirect |
| 3. C2×#66561 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 5. #10620503 | C2 | semidirect |
| 13. C2×C3×D28 | C22 | semidirect |
| 14. C2×C7×C3⋊C8 | C22 | semidirect |
| 16. C3×C4⋊Dic7 | C22 | semidirect |
| 19. #6493 | D3 | semidirect |
| 35. D84 | D4 | semidirect |
| 46. C2×D28 | C2×D3 | semidirect |
| 49. C4⋊Dic7 | C2×D3 | semidirect |
| 54. #830 | D7 | semidirect |
| 58. C22×C3×C7 | D8 | semidirect |
| 97. C2×C3⋊C8 | C2×D7 | semidirect |
| 111. C22×C7 | #213 | semidirect |
| 139. C3×C7 | #447 | semidirect |
| 162. C22×C3 | D56 | semidirect |
| 187. C7 | #5036 | semidirect |
| 203. C22 | #66561 | semidirect |
| 208. C3 | #89504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C3×#6493 | 2 |
| C2×#66561 | 2 |
| C7×#830 | 2 |
| #10620503 | 2 |
| #89504 | 3 |
| #5036 | 7 |