Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1067 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1067 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 13. #88540 | C4 | direct (N × H) |
| 15. C4×#1084 | C4 | semidirect |
| 52. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 55. #1084 | C42 | semidirect |
| 110. C32×C4 | Dic3⋊C4 | semidirect |
| 119. H(3,𝔽3) | C4×C4⋊C4 | semidirect |
| 182. C32 | C4×Dic3⋊C4 | semidirect |
| 216. C4 | #88540 | direct (N × H) |
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×#88540 | 2 |
| C2×C4×#1084 | 2 |
| #11720574 | 2 |
| C3×C4×Dic3⋊C4 | 3 |