Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
122 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 8. C3⋊#3708 | C4 | semidirect |
| 61. C33 | #367 | semidirect |
| 93. C32 | #4490 | semidirect |
| 113. C3 | #10590086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723094 | 2 |
| #11723089 | 2 |
| C3×#63769 | 2 |
| #10590086 | 3 |
| #4490 | 9 |