Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
536 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 536 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×H(5,𝔽2) | C2 | semidirect |
| 2. C3×#6553 | C2 | semidirect |
| 3. C3×#6513 | C2 | semidirect |
| 4. C3×#6512 | C2 | semidirect |
| 5. C3×#6511 | C2 | semidirect |
| 6. C3×#6495 | C2 | semidirect |
| 7. C2×C3×#1141 | C2 | semidirect |
| 8. #90526 | C3 | direct (N × H) |
| 11. C3×C7×#41 | C22 | semidirect |
| 13. C2×C3×C7×D4 | C22 | semidirect |
| 16. C3×#1157 | C22 | semidirect |
| 17. C2×C3×D28 | C22 | semidirect |
| 18. C3×#1144 | C22 | semidirect |
| 19. C3×#1143 | C22 | semidirect |
| 20. C3×#1142 | C22 | semidirect |
| 21. C3×#1141 | C22 | semidirect |
| 22. C3×#1141 | C22 | semidirect |
| 23. C3×#1136 | C22 | semidirect |
| 24. C2×C3×C7⋊C8 | C22 | semidirect |
| 25. C7×H(5,𝔽2) | C2×C3 | semidirect |
| 26. #6553 | C2×C3 | semidirect |
| 27. #6513 | C2×C3 | semidirect |
| 28. #6512 | C2×C3 | semidirect |
| 29. #6511 | C2×C3 | semidirect |
| 30. #6495 | C2×C3 | semidirect |
| 31. C2×#1141 | C2×C3 | semidirect |
| 52. C7×#41 | C22×C3 | semidirect |
| 54. C2×C7×D4 | C22×C3 | semidirect |
| 57. #1157 | C22×C3 | semidirect |
| 58. C2×D28 | C22×C3 | semidirect |
| 59. #1144 | C22×C3 | semidirect |
| 60. #1143 | C22×C3 | semidirect |
| 61. #1142 | C22×C3 | semidirect |
| 62. #1141 | C22×C3 | semidirect |
| 63. #1141 | C22×C3 | semidirect |
| 64. #1136 | C22×C3 | semidirect |
| 65. C2×C7⋊C8 | C22×C3 | semidirect |
| 67. C3×H(5,𝔽2) | D7 | semidirect |
| 104. C3×#41 | C2×D7 | semidirect |
| 108. C2×C3×D4 | C2×D7 | semidirect |
| 121. H(5,𝔽2) | C3×D7 | semidirect |
| 153. C3×C7 | #576 | semidirect |
| 158. #41 | C2×C3×D7 | semidirect |
| 162. C2×D4 | C2×C3×D7 | semidirect |
| 200. C7 | C3×#576 | semidirect |
| 214. C3 | #90526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×H(5,𝔽2) | 2 |
| C3×#6553 | 2 |
| C3×#6513 | 2 |
| C3×#6512 | 2 |
| C3×#6511 | 2 |
| C3×#6495 | 2 |
| C2×C3×#1141 | 2 |
| #90526 | 3 |
| C3×#576 | 7 |