Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
787 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 787 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
| 12. #88449 | C4 | direct (N × H) |
| 50. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 52. #1084 | C42 | semidirect |
| 123. C32×C4 | Dic3⋊C4 | semidirect |
| 134. H(3,𝔽3) | C4×C4⋊C4 | semidirect |
| 213. C32 | C4×Dic3⋊C4 | semidirect |
| 248. C4 | #88449 | direct (N × H) |
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×#88449 | 2 |
| #11720334 | 2 |
| C4×Dic3⋊Dic3 | 3 |