Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1023 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1023 conjugacy classes of subgroups — too many to draw. Only its 245 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. C4×#1084 | C4 | semidirect |
| 45. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 47. #1084 | C4⋊C4 | semidirect |
| 95. C32×C4 | Dic3⋊C4 | semidirect |
| 102. H(3,𝔽3) | #384 | semidirect |
| 156. C32 | #4975 | semidirect |
| 186. C4 | #88540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C2×C4⋊#1084 | 2 |
| C2×#88540 | 2 |
| C2×C4×#1084 | 2 |
| C3×#4975 | 3 |