Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10621431 | C2 | semidirect |
| 3. #10620846 | C2 | semidirect |
| 4. C7×#837 | C2 | semidirect |
| 5. #10620526 | C2 | semidirect |
| 6. #10620512 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 17. C3×#1144 | C4 | semidirect |
| 18. C3×#1143 | C4 | semidirect |
| 19. C3×#1142 | C4 | semidirect |
| 20. C3×#1141 | C4 | semidirect |
| 52. #1144 | Dic3 | semidirect |
| 53. #1143 | Dic3 | semidirect |
| 54. #1142 | Dic3 | semidirect |
| 55. #1141 | Dic3 | semidirect |
| 67. #837 | D7 | semidirect |
| 145. C3×C7 | #443 | semidirect |
| 189. C7 | #5196 | semidirect |
| 202. C3 | #89596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621431 | 2 |
| C3×#6513 | 2 |
| #10620846 | 2 |
| C7×#837 | 2 |
| #10620526 | 2 |
| #10620512 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89596 | 3 |
| #5196 | 7 |