Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 208 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 |
|---|---|---|
| 2. C3×#6511 | C2 | semidirect |
| 3. #10620848 | C2 | semidirect |
| 4. #10620676 | C2 | semidirect |
| 5. #10620528 | C2 | semidirect |
| 6. #10620513 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 13. C7×#216 | C4 | semidirect |
| 14. C7×#215 | C4 | semidirect |
| 15. C7×#214 | C4 | semidirect |
| 16. C7×#213 | C4 | semidirect |
| 26. #6511 | D3 | semidirect |
| 101. #216 | Dic7 | semidirect |
| 102. #215 | Dic7 | semidirect |
| 103. #214 | Dic7 | semidirect |
| 104. #213 | Dic7 | semidirect |
| 145. C3×C7 | #444 | semidirect |
| 189. C7 | #5145 | semidirect |
| 202. C3 | #89969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#950 | 2 |
| C3×#6511 | 2 |
| #10620848 | 2 |
| #10620676 | 2 |
| #10620528 | 2 |
| #10620513 | 2 |
| #10620489 | 2 |
| #89969 | 3 |
| #5145 | 7 |