Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 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×#64545 | C2 | semidirect |
| 2. C3×#64543 | C2 | semidirect |
| 3. C3×SD16×C19 | C2 | semidirect |
| 4. C3×#64528 | C2 | semidirect |
| 5. C3×#64525 | C2 | semidirect |
| 6. C3×#64516 | C2 | semidirect |
| 7. C3×C8×D19 | C2 | semidirect |
| 8. #10597362 | C3 | direct (N × H) |
| 20. #64545 | C2×C3 | semidirect |
| 21. #64543 | C2×C3 | semidirect |
| 22. SD16×C19 | C2×C3 | semidirect |
| 23. #64528 | C2×C3 | semidirect |
| 24. #64525 | C2×C3 | semidirect |
| 25. #64516 | C2×C3 | semidirect |
| 26. C8×D19 | C2×C3 | semidirect |
| 57. C3×C19 | #135 | semidirect |
| 62. C3×SD16 | D19 | semidirect |
| 81. C19 | C3×#135 | semidirect |
| 86. SD16 | C3×D19 | semidirect |
| 118. C3 | #10597362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64545 | 2 |
| C3×#64543 | 2 |
| C3×SD16×C19 | 2 |
| C3×#64528 | 2 |
| C3×#64525 | 2 |
| C3×#64516 | 2 |
| C3×C8×D19 | 2 |
| #10597362 | 3 |
| C3×#135 | 19 |