Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
146 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 24. C3×C3⋊Dic3 | C16 | semidirect |
| 54. C3⋊Dic3 | C3⋊C16 | semidirect |
| 62. C33 | C4⋊C16 | semidirect |
| 100. C32 | C4⋊(C3⋊C16) | semidirect |
| 123. C3 | #10593265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#3771 | 2 |
| C3×C4×#622 | 2 |
| #10593265 | 3 |
| C4⋊(C3⋊C16) | 9 |