Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
420 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 92 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. D3×C22⋊Dic7 | C2 | semidirect |
| 3. #10620673 | C2 | semidirect |
| 4. C3×#6408 | C2 | semidirect |
| 5. #10620531 | C2 | semidirect |
| 7. C23×D3×C7 | C4 | semidirect |
| 10. C2×C7×#67 | C4 | semidirect |
| 14. C2×C7×D12 | C4 | semidirect |
| 15. C2×C4×D3×C7 | C4 | semidirect |
| 17. #66636 | C22 | semidirect |
| 18. C3×C22⋊Dic7 | C22 | semidirect |
| 24. #6408 | D3 | direct (N × H) |
| 26. C23×C3×C7 | C2×C4 | semidirect |
| 34. C22×D3×C7 | C2×C4 | semidirect |
| 38. C2×C3×C4×C7 | C2×C4 | semidirect |
| 42. C2×C7×Dic3 | C2×C4 | semidirect |
| 60. C22⋊Dic7 | C2×D3 | semidirect |
| 96. C23×C7 | C4×D3 | semidirect |
| 105. C2×C4×C7 | C4×D3 | semidirect |
| 109. C23×D3 | Dic7 | semidirect |
| 112. C2×#67 | Dic7 | semidirect |
| 116. C2×D12 | Dic7 | semidirect |
| 118. C2×C4×D3 | Dic7 | semidirect |
| 129. D3×C7 | #99 | semidirect |
| 155. C23×C3 | C2×Dic7 | semidirect |
| 163. C22×D3 | C2×Dic7 | semidirect |
| 168. C2×C3×C4 | C2×Dic7 | semidirect |
| 172. C2×Dic3 | C2×Dic7 | semidirect |
| 177. C3×C7 | C2×#99 | semidirect |
| 228. C23 | D3×Dic7 | semidirect |
| 240. C2×C4 | D3×Dic7 | semidirect |
| 241. C7 | D3×#99 | semidirect |
| 249. D3 | #6408 | direct (N × H) |
| 270. C3 | C2×#6408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| D3×C22⋊Dic7 | 2 |
| #10620673 | 2 |
| C3×#6408 | 2 |
| #10620531 | 2 |
| C2×#6408 | 3 |
| D3×#99 | 7 |