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. D8×D21 | C2 | semidirect |
| 2. #10620841 | C2 | semidirect |
| 3. C7×#826 | C2 | semidirect |
| 4. C3×#6401 | C2 | semidirect |
| 5. #10620478 | C2 | semidirect |
| 6. #10620474 | C2 | semidirect |
| 7. #10620471 | C2 | semidirect |
| 15. C7×D24 | C22 | semidirect |
| 16. C3×Dic28 | C22 | semidirect |
| 18. C3×C7⋊C16 | C22 | semidirect |
| 19. C7×C3⋊C16 | C22 | semidirect |
| 23. #6401 | D3 | semidirect |
| 45. Dic28 | C2×D3 | semidirect |
| 49. C7⋊C16 | C2×D3 | semidirect |
| 54. #826 | D7 | semidirect |
| 84. D24 | C2×D7 | semidirect |
| 87. C3⋊C16 | C2×D7 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 155. C7 | #4914 | semidirect |
| 169. C3 | #89683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D21 | 2 |
| #10620841 | 2 |
| C7×#826 | 2 |
| C3×#6401 | 2 |
| #10620478 | 2 |
| #10620474 | 2 |
| #10620471 | 2 |
| #89683 | 3 |
| #4914 | 7 |