Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 122 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. #11722189 | C2 | semidirect |
| 3. C32×#812 | C2 | semidirect |
| 18. C3×#812 | D3 | semidirect |
| 53. #812 | C3⋊D3 | semidirect |
| 106. C33 | #361 | semidirect |
| 153. C32 | #4516 | semidirect |
| 154. C32 | #4563 | semidirect |
| 176. C3 | #10589127 | semidirect |
| 177. C3 | #10589382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| #11722189 | 2 |
| C32×#812 | 2 |
| #10589382 | 3 |
| #10589127 | 3 |