Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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. #10621390 | C2 | semidirect |
| 3. C3×C7×#108 | C2 | semidirect |
| 4. #10620664 | C2 | semidirect |
| 5. #10620654 | C2 | semidirect |
| 12. Dic84 | C4 | semidirect |
| 13. D168 | C4 | semidirect |
| 14. #66623 | C4 | semidirect |
| 19. C7×#108 | D3 | semidirect |
| 45. C3×#108 | D7 | semidirect |
| 80. #108 | D21 | semidirect |
| 99. C3×C7 | #444 | semidirect |
| 129. C7 | #4894 | semidirect |
| 139. C3 | #89666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621390 | 2 |
| #10621387 | 2 |
| C3×C7×#108 | 2 |
| #10620664 | 2 |
| #10620654 | 2 |
| #89666 | 3 |
| #4894 | 7 |