Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C3×Q8×D19 | C2 | semidirect |
| 3. C3×Q16×C19 | C2 | semidirect |
| 4. C3×#64528 | C2 | semidirect |
| 5. C3×#64527 | C2 | semidirect |
| 6. C3×#64516 | C2 | semidirect |
| 7. C3×#64515 | C2 | semidirect |
| 8. #10597364 | C3 | direct (N × H) |
| 21. Q8×D19 | C2×C3 | semidirect |
| 22. Q16×C19 | C2×C3 | semidirect |
| 23. #64528 | C2×C3 | semidirect |
| 24. #64527 | C2×C3 | semidirect |
| 25. #64516 | C2×C3 | semidirect |
| 26. #64515 | C2×C3 | semidirect |
| 56. C3×C19 | #137 | semidirect |
| 60. C3×Q16 | D19 | semidirect |
| 79. C19 | C3×#137 | semidirect |
| 83. Q16 | C3×D19 | semidirect |
| 115. C3 | #10597364 | 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×Q8×D19 | 2 |
| C3×Q16×C19 | 2 |
| C3×#64528 | 2 |
| C3×#64527 | 2 |
| C3×#64516 | 2 |
| C3×#64515 | 2 |
| #10597364 | 3 |
| C3×#137 | 19 |