Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
591 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 591 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 |
|---|---|---|
| 3. #10592636 | C3 | semidirect |
| 7. C42×H(3,𝔽3) | C4 | semidirect |
| 26. C32×C42 | Dic3 | semidirect |
| 27. C32×C42 | C3×C4 | semidirect |
| 77. H(3,𝔽3) | #383 | semidirect |
| 101. C42 | (C3⋊Dic3)⋊C3 | semidirect |
| 118. C32 | #4937 | semidirect |
| 119. C32 | C3×#383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×H(3,𝔽3) | 2 |
| #63658⋊C3 | 2 |
| #10592636 | 3 |
| C3×#4937 | 3 |