Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10621395 | C2 | semidirect |
| 2. #10620818 | C2 | semidirect |
| 3. C7×#826 | C2 | semidirect |
| 4. C3×#6400 | C2 | semidirect |
| 5. #10620479 | C2 | semidirect |
| 6. #10620477 | C2 | semidirect |
| 7. #10620471 | C2 | semidirect |
| 11. C3×C7×D8 | C22 | semidirect |
| 13. Dic84 | C22 | semidirect |
| 18. C3×C7⋊C16 | C22 | semidirect |
| 19. C7×C3⋊C16 | C22 | semidirect |
| 24. #6400 | D3 | semidirect |
| 42. C7×D8 | C2×D3 | semidirect |
| 49. C7⋊C16 | C2×D3 | semidirect |
| 54. #826 | D7 | semidirect |
| 80. C3×D8 | C2×D7 | semidirect |
| 87. C3⋊C16 | C2×D7 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 127. D8 | D3×D7 | semidirect |
| 155. C7 | #4911 | semidirect |
| 169. C3 | #89683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621395 | 2 |
| #10620818 | 2 |
| C7×#826 | 2 |
| C3×#6400 | 2 |
| #10620479 | 2 |
| #10620477 | 2 |
| #10620471 | 2 |
| #89683 | 3 |
| #4911 | 7 |