Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 214 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. C3×C7×2−1+4 | C2 | semidirect |
| 2. C7×#1009 | C2 | semidirect |
| 3. C7×#950 | C2 | semidirect |
| 4. C7×#949 | C2 | semidirect |
| 5. C7×#948 | C2 | semidirect |
| 6. C7×#942 | C2 | semidirect |
| 7. C2×C7×#215 | C2 | semidirect |
| 11. C3×C7×#41 | C22 | semidirect |
| 13. C2×C3×C7×Q8 | C22 | semidirect |
| 18. C7×#216 | C22 | semidirect |
| 19. C7×#215 | C22 | semidirect |
| 20. C7×#215 | C22 | semidirect |
| 21. C7×#214 | C22 | semidirect |
| 22. C7×#213 | C22 | semidirect |
| 23. C7×#208 | C22 | semidirect |
| 24. C2×C7×C3⋊C8 | C22 | semidirect |
| 25. C7×2−1+4 | D3 | semidirect |
| 32. #5837 | C7 | direct (N × H) |
| 54. C7×#41 | C2×D3 | semidirect |
| 56. C2×C7×Q8 | C2×D3 | semidirect |
| 66. C3×2−1+4 | C2×C7 | semidirect |
| 67. #1009 | C2×C7 | semidirect |
| 68. #950 | C2×C7 | semidirect |
| 69. #949 | C2×C7 | semidirect |
| 70. #948 | C2×C7 | semidirect |
| 71. #942 | C2×C7 | semidirect |
| 72. C2×#215 | C2×C7 | semidirect |
| 101. C3×#41 | C22×C7 | semidirect |
| 103. C2×C3×Q8 | C22×C7 | semidirect |
| 108. #216 | C22×C7 | semidirect |
| 109. #215 | C22×C7 | semidirect |
| 110. #215 | C22×C7 | semidirect |
| 111. #214 | C22×C7 | semidirect |
| 112. #213 | C22×C7 | semidirect |
| 113. #208 | C22×C7 | semidirect |
| 114. C2×C3⋊C8 | C22×C7 | semidirect |
| 119. 2−1+4 | D3×C7 | semidirect |
| 151. C3×C7 | #577 | semidirect |
| 156. #41 | C2×D3×C7 | semidirect |
| 158. C2×Q8 | C2×D3×C7 | semidirect |
| 197. C7 | #5837 | direct (N × H) |
| 210. C3 | C7×#577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×2−1+4 | 2 |
| C7×#1009 | 2 |
| C7×#950 | 2 |
| C7×#949 | 2 |
| C7×#948 | 2 |
| C7×#942 | 2 |
| C2×C7×#215 | 2 |
| C7×#577 | 3 |
| #5837 | 7 |