Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
620 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 208 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. C7×#926 | C2 | semidirect |
| 3. C2×C3×C4×Dic7 | C2 | semidirect |
| 4. #10621114 | C2 | semidirect |
| 5. #10620980 | C2 | semidirect |
| 6. C4×D21⋊C4 | C2 | semidirect |
| 7. #10620948 | C2 | semidirect |
| 8. #10620895 | C2 | semidirect |
| 12. #66728 | C4 | semidirect |
| 29. C2×C4×Dic7 | D3 | semidirect |
| 38. C2×C3×C4×C7 | C2×C4 | semidirect |
| 41. #4268 | C2×C4 | semidirect |
| 43. D84 | C2×C4 | semidirect |
| 44. C4×D21 | C2×C4 | semidirect |
| 45. Dic42 | C2×C4 | semidirect |
| 71. #926 | D7 | semidirect |
| 85. C3×Dic7 | #41 | semidirect |
| 91. C2×C4×C7 | C4×D3 | semidirect |
| 142. Dic7 | #235 | semidirect |
| 148. C2×C3×C4 | C4×D7 | semidirect |
| 158. C3×C7 | C4×#41 | semidirect |
| 203. C2×C4 | D21⋊C4 | semidirect |
| 206. C7 | C4×#235 | semidirect |
| 222. C3 | #90213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C7×#926 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #10621114 | 2 |
| #10620980 | 2 |
| C4×D21⋊C4 | 2 |
| #10620948 | 2 |
| #10620895 | 2 |
| #90213 | 3 |
| C4×#235 | 7 |