Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1780 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 1780 conjugacy classes of subgroups — too many to draw. Only its 619 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. C23×C3×C4×C7 | C2 | semidirect |
| 2. C22×#4268 | C2 | semidirect |
| 3. C2×#66728 | C2 | direct (N × H) |
| 4. C22×D84 | C2 | semidirect |
| 5. C22×C4×D21 | C2 | semidirect |
| 6. C22×Dic42 | C2 | semidirect |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 13. C2×#4268 | C22 | semidirect |
| 15. #66728 | C22 | direct (N × H) |
| 16. C2×D84 | C22 | semidirect |
| 17. C2×C4×D21 | C22 | semidirect |
| 18. C2×Dic42 | C22 | semidirect |
| 19. C23×C4×C7 | D3 | semidirect |
| 33. C2×C3×C4×C7 | C23 | semidirect |
| 34. #4268 | C23 | semidirect |
| 36. D84 | C23 | semidirect |
| 37. C4×D21 | C23 | semidirect |
| 38. Dic42 | C23 | semidirect |
| 43. C22×C4×C7 | C2×D3 | semidirect |
| 50. C23×C3×C4 | D7 | semidirect |
| 57. C22×C3×C7 | #41 | semidirect |
| 73. C2×C4×C7 | C22×D3 | semidirect |
| 83. C22×C3×C4 | C2×D7 | semidirect |
| 91. C2×C3×C7 | C2×#41 | semidirect |
| 99. C23×C4 | D21 | semidirect |
| 101. C22×C7 | #235 | semidirect |
| 116. C2×C3×C4 | C22×D7 | semidirect |
| 122. C3×C7 | C22×#41 | semidirect |
| 133. C22×C4 | C2×D21 | semidirect |
| 135. C2×C7 | C2×#235 | semidirect |
| 139. C22×C3 | #1157 | semidirect |
| 159. C2×C4 | C22×D21 | semidirect |
| 160. C7 | C22×#235 | semidirect |
| 162. C2×C3 | C2×#1157 | semidirect |
| 168. C22 | #66728 | direct (N × H) |
| 174. C3 | C22×#1157 | semidirect |
| 177. C2 | C2×#66728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C7 | 2 |
| C22×#4268 | 2 |
| C2×#66728 | 2 |
| C22×D84 | 2 |
| C22×C4×D21 | 2 |
| C22×Dic42 | 2 |
| C22×#1157 | 3 |
| C22×#235 | 7 |