Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 407 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 |
|---|---|---|
| 35. C33×C8 | Q8 | semidirect |
| 36. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 73. C32×C8 | Dic6 | semidirect |
| 106. C33 | #501 | semidirect |
| 115. C3×C8 | #634 | semidirect |
| 140. C32 | #4856 | semidirect |
| 150. C8 | #6308 | semidirect |
| 163. C3 | #10592555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723931 | 2 |
| #11723929 | 2 |
| C33×#106 | 2 |
| #11722188 | 2 |
| #11722185 | 2 |
| #11722178 | 2 |
| #11722177 | 2 |
| #10592555 | 3 |