Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
787 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 787 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 10. C4×#1084 | C4 | semidirect |
| 11. C4⋊((C3⋊Dic3)⋊C3) | C4 | semidirect |
| 40. C4⋊(C3⋊Dic3) | Dic3 | semidirect |
| 50. C4×H(3,𝔽3) | C42 | semidirect |
| 52. #1084 | C4⋊C4 | semidirect |
| 127. C32×C4 | C4×Dic3 | semidirect |
| 138. H(3,𝔽3) | C4×C4⋊C4 | semidirect |
| 223. C32 | Dic3×C4⋊C4 | semidirect |
| 260. C4 | #88447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1084 | 2 |
| C2×C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×#88447 | 2 |
| #11720334 | 2 |
| Dic3×C4⋊Dic3 | 3 |