Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 30. C3×C3⋊Dic3 | C16 | semidirect |
| 70. C3⋊Dic3 | C3⋊C16 | semidirect |
| 75. C33 | C4⋊C16 | semidirect |
| 118. C32 | C4⋊(C3⋊C16) | semidirect |
| 141. C3 | #10590177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#3708 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10590177 | 3 |
| C4⋊(C3⋊C16) | 9 |