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. #10620850 | C2 | semidirect |
| 4. C3×#6411 | C2 | semidirect |
| 5. #10620528 | C2 | semidirect |
| 6. #10620514 | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 15. C7×#216 | C4 | semidirect |
| 16. C7×#215 | C4 | semidirect |
| 17. C7×#214 | C4 | semidirect |
| 18. C7×#213 | C4 | semidirect |
| 28. #6411 | D3 | semidirect |
| 99. #216 | Dic7 | semidirect |
| 100. #215 | Dic7 | semidirect |
| 101. #214 | Dic7 | semidirect |
| 102. #213 | Dic7 | semidirect |
| 145. C3×C7 | #443 | semidirect |
| 189. C7 | #4824 | semidirect |
| 202. C3 | #89968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621431 | 2 |
| C7×#950 | 2 |
| #10620850 | 2 |
| C3×#6411 | 2 |
| #10620528 | 2 |
| #10620514 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89968 | 3 |
| #4824 | 7 |