Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
684 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
| 3. C2×C7×#217 | C2 | semidirect |
| 4. C7×#929 | C2 | direct (N × H) |
| 5. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 17. C7×#217 | C22 | semidirect |
| 18. C7×(C2×D3)⋊C4 | C22 | semidirect |
| 19. C7×Dic3⋊C4 | C22 | semidirect |
| 21. C23×C4×C7 | D3 | semidirect |
| 26. C2×#929 | C7 | direct (N × H) |
| 50. C22×C4×C7 | C2×D3 | semidirect |
| 54. C23×C3×C4 | C2×C7 | semidirect |
| 56. C2×#217 | C2×C7 | semidirect |
| 57. #929 | C2×C7 | direct (N × H) |
| 58. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 59. C2×Dic3⋊C4 | C2×C7 | semidirect |
| 92. C22×C3×C4 | C22×C7 | semidirect |
| 97. #217 | C22×C7 | semidirect |
| 98. (C2×D3)⋊C4 | C22×C7 | semidirect |
| 99. Dic3⋊C4 | C22×C7 | semidirect |
| 101. C2×C3×C7 | #123 | semidirect |
| 106. C23×C4 | D3×C7 | semidirect |
| 138. C3×C7 | C2×#123 | semidirect |
| 147. C22×C4 | C2×D3×C7 | semidirect |
| 153. C2×C7 | #929 | direct (N × H) |
| 183. C7 | C2×#929 | direct (N × H) |
| 185. C2×C3 | C7×#123 | semidirect |
| 201. C3 | C2×C7×#123 | semidirect |
| 204. C2 | C7×#929 | 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×C7×#67 | 2 |
| C2×C7×#217 | 2 |
| C7×#929 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C2×C7×#123 | 3 |
| C2×#929 | 7 |