Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1023 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1023 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 6. C42×H(3,𝔽3) | C4 | semidirect |
| 19. C32×C42 | Dic3 | semidirect |
| 24. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 50. C32×C4 | C4⋊Dic3 | semidirect |
| 54. H(3,𝔽3) | #384 | semidirect |
| 71. C42 | #1084 | semidirect |
| 82. C32 | #4935 | semidirect |
| 98. C4 | C4⋊#1084 | 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 |
| C2×C4⋊#1084 | 2 |
| C3×#4935 | 3 |