Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1796 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1796 conjugacy classes of subgroups — too many to draw. Only its 587 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. C2×C3×C7×#41 | C2 | semidirect |
| 2. #10621662 | C2 | direct (N × H) |
| 3. C2×#66732 | C2 | semidirect |
| 4. C2×D4×D21 | C2 | semidirect |
| 5. C2×#66728 | C2 | semidirect |
| 6. C22×D84 | C2 | semidirect |
| 8. C23×D21 | C22 | semidirect |
| 9. C3×C7×#41 | C22 | semidirect |
| 10. C2×C3×C7×Q8 | C22 | semidirect |
| 11. C2×C3×C7×D4 | C22 | semidirect |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 13. C2×#4268 | C22 | semidirect |
| 14. #66732 | C22 | semidirect |
| 15. D4×D21 | C22 | semidirect |
| 16. #66728 | C22 | semidirect |
| 17. C2×D84 | C22 | semidirect |
| 18. C2×D84 | C22 | semidirect |
| 19. C2×D84 | C22 | semidirect |
| 20. C2×C4×D21 | C22 | semidirect |
| 21. C2×Dic42 | C22 | semidirect |
| 22. C2×C7×#41 | D3 | semidirect |
| 32. C22×D21 | C23 | semidirect |
| 33. C3×C7×Q8 | C23 | semidirect |
| 34. C3×C7×D4 | C23 | semidirect |
| 37. C2×C3×C4×C7 | C23 | semidirect |
| 38. #4268 | C23 | semidirect |
| 40. D84 | C23 | semidirect |
| 41. D84 | C23 | semidirect |
| 42. C4×D21 | C23 | semidirect |
| 43. Dic42 | C23 | semidirect |
| 45. C7×#41 | C2×D3 | semidirect |
| 46. C2×C7×Q8 | C2×D3 | semidirect |
| 47. C2×C7×D4 | C2×D3 | semidirect |
| 48. C22×C4×C7 | C2×D3 | semidirect |
| 58. C2×C3×#41 | D7 | semidirect |
| 78. C7×Q8 | C22×D3 | semidirect |
| 79. C7×D4 | C22×D3 | semidirect |
| 82. C2×C4×C7 | C22×D3 | semidirect |
| 90. C3×#41 | C2×D7 | semidirect |
| 91. C2×C3×Q8 | C2×D7 | semidirect |
| 92. C2×C3×D4 | C2×D7 | semidirect |
| 93. C22×C3×C4 | C2×D7 | semidirect |
| 104. C2×C3×C7 | H(5,𝔽2) | semidirect |
| 110. C2×#41 | D21 | semidirect |
| 126. C3×Q8 | C22×D7 | semidirect |
| 127. C3×D4 | C22×D7 | semidirect |
| 130. C2×C3×C4 | C22×D7 | semidirect |
| 137. C3×C7 | C2×H(5,𝔽2) | semidirect |
| 141. #41 | C2×D21 | semidirect |
| 143. C2×Q8 | C2×D21 | semidirect |
| 149. C2×D4 | C2×D21 | semidirect |
| 151. C22×C4 | C2×D21 | semidirect |
| 153. C2×C7 | #1009 | semidirect |
| 170. Q8 | C22×D21 | semidirect |
| 174. D4 | C22×D21 | semidirect |
| 179. C2×C4 | C22×D21 | semidirect |
| 180. C7 | C2×#1009 | semidirect |
| 182. C2×C3 | #6553 | semidirect |
| 194. C3 | C2×#6553 | semidirect |
| 197. C2 | #10621662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| #10621662 | 2 |
| C2×#66732 | 2 |
| C2×D4×D21 | 2 |
| C2×#66728 | 2 |
| C22×D84 | 2 |
| C2×#6553 | 3 |
| C2×#1009 | 7 |