Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 382 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 |
|---|---|---|
| 3. #10592636 | C3 | direct (N × H) |
| 7. C33×C42 | C4 | semidirect |
| 25. C32×C42 | Dic3 | semidirect |
| 26. C32×C42 | C3×C4 | semidirect |
| 56. C3×C42 | C3×Dic3 | semidirect |
| 57. C3×C42 | C3⋊Dic3 | semidirect |
| 71. C33 | #383 | semidirect |
| 91. C42 | C3×C3⋊Dic3 | semidirect |
| 104. C32 | #4937 | semidirect |
| 105. C32 | C3×#383 | semidirect |
| 121. C3 | C3×#4937 | semidirect |
| 122. C3 | #10592636 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C42 | 2 |
| C3×#63658 | 2 |
| #10592636 | 3 |
| C3×#4937 | 3 |