Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
351 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10592575 | C3 | semidirect |
| 44. C8×H(3,𝔽3) | Q8 | semidirect |
| 45. (C3⋊(C3⋊C8))⋊C3 | Q8 | semidirect |
| 125. C32×C8 | Dic6 | semidirect |
| 126. C32×C8 | C3×Q8 | semidirect |
| 127. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 199. H(3,𝔽3) | #501 | semidirect |
| 287. C32 | #4876 | semidirect |
| 288. C32 | C3×#501 | semidirect |
| 298. C8 | #634⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64099⋊C3 | 2 |
| #64097⋊C3 | 2 |
| H(3,𝔽3)×#107 | 2 |
| #63644⋊C3 | 2 |
| #63642⋊C3 | 2 |
| #63635⋊C3 | 2 |
| #63634⋊C3 | 2 |
| #10592575 | 3 |
| C3×#4876 | 3 |