Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
812 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 172 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. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 97. C3⋊(C3⋊C8) | Dic6 | semidirect |
| 149. C33 | #501 | semidirect |
| 209. C32 | #4702 | semidirect |
| 210. C32 | #5064 | semidirect |
| 236. C3 | #10590306 | semidirect |
| 237. C3 | #10592763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C32×#870 | 2 |
| C3×#63630 | 2 |
| #11722057 | 2 |
| #11722054 | 2 |
| #10592763 | 3 |
| #10590306 | 3 |