Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×Q8×D19 | C2 | semidirect |
| 3. C3×SD16×C19 | C2 | semidirect |
| 4. C3×#64527 | C2 | semidirect |
| 5. C3×#64526 | C2 | semidirect |
| 6. C3×#64516 | C2 | semidirect |
| 7. C3×C8×D19 | C2 | semidirect |
| 8. SD16×D19 | C3 | direct (N × H) |
| 10. C3×Q8×C19 | C22 | semidirect |
| 17. C3×Dic38 | C22 | semidirect |
| 18. C3×C8×C19 | C22 | semidirect |
| 19. C3×C19⋊C8 | C22 | semidirect |
| 20. Q8×D19 | C2×C3 | semidirect |
| 22. SD16×C19 | C2×C3 | semidirect |
| 23. #64527 | C2×C3 | semidirect |
| 24. #64526 | C2×C3 | semidirect |
| 25. #64516 | C2×C3 | semidirect |
| 26. C8×D19 | C2×C3 | semidirect |
| 36. Q8×C19 | C22×C3 | semidirect |
| 43. Dic38 | C22×C3 | semidirect |
| 44. C8×C19 | C22×C3 | semidirect |
| 45. C19⋊C8 | C22×C3 | semidirect |
| 49. C3×D19 | SD16 | direct (N × H) |
| 59. C3×C19 | C2×SD16 | semidirect |
| 65. C3×SD16 | D19 | direct (N × H) |
| 70. D19 | C3×SD16 | direct (N × H) |
| 75. C3×Q8 | C2×D19 | semidirect |
| 82. C3×C8 | C2×D19 | semidirect |
| 83. C19 | C2×C3×SD16 | semidirect |
| 89. SD16 | C3×D19 | direct (N × H) |
| 102. Q8 | C2×C3×D19 | semidirect |
| 109. C8 | C2×C3×D19 | semidirect |
| 122. C3 | SD16×D19 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D19 | 2 |
| C3×D4×D19 | 2 |
| C3×SD16×C19 | 2 |
| C3×#64527 | 2 |
| C3×#64526 | 2 |
| C3×#64516 | 2 |
| C3×C8×D19 | 2 |
| SD16×D19 | 3 |
| C2×C3×SD16 | 19 |