Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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×#64543 | C2 | semidirect |
| 2. C3×D4×D19 | C2 | semidirect |
| 3. C3×D8×C19 | C2 | semidirect |
| 4. C3×#64526 | C2 | semidirect |
| 5. C3×#64525 | C2 | semidirect |
| 6. C3×#64516 | C2 | semidirect |
| 7. C3×#64515 | C2 | semidirect |
| 8. #10597357 | C3 | direct (N × H) |
| 11. C3×D4×C19 | C22 | semidirect |
| 17. C3×Dic38 | C22 | semidirect |
| 18. C3×C8×C19 | C22 | semidirect |
| 19. C3×C19⋊C8 | C22 | semidirect |
| 20. #64543 | C2×C3 | semidirect |
| 21. D4×D19 | C2×C3 | semidirect |
| 22. D8×C19 | C2×C3 | semidirect |
| 23. #64526 | C2×C3 | semidirect |
| 24. #64525 | C2×C3 | semidirect |
| 25. #64516 | C2×C3 | semidirect |
| 26. #64515 | C2×C3 | semidirect |
| 37. D4×C19 | C22×C3 | semidirect |
| 43. Dic38 | C22×C3 | semidirect |
| 44. C8×C19 | C22×C3 | semidirect |
| 45. C19⋊C8 | C22×C3 | semidirect |
| 60. C3×C19 | AGL(1,ℤ/8) | semidirect |
| 66. C3×D8 | D19 | semidirect |
| 80. C3×D4 | C2×D19 | semidirect |
| 84. C3×C8 | C2×D19 | semidirect |
| 85. C19 | C3×AGL(1,ℤ/8) | semidirect |
| 91. D8 | C3×D19 | semidirect |
| 107. D4 | C2×C3×D19 | semidirect |
| 111. C8 | C2×C3×D19 | semidirect |
| 125. C3 | #10597357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64543 | 2 |
| C3×D4×D19 | 2 |
| C3×D8×C19 | 2 |
| C3×#64526 | 2 |
| C3×#64525 | 2 |
| C3×#64516 | 2 |
| C3×#64515 | 2 |
| #10597357 | 3 |
| C3×AGL(1,ℤ/8) | 19 |