Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
660 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #11721715 | C2 | semidirect |
| 4. #11720532 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 52. C4×H(3,𝔽3) | SD16 | semidirect |
| 109. C32×C4 | #214 | semidirect |
| 118. H(3,𝔽3) | #461 | semidirect |
| 177. C32 | #5019 | semidirect |
| 205. C4 | #88546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| C2×#88546 | 2 |
| #11721715 | 2 |
| #11720532 | 2 |
| C4⋊#6180 | 2 |
| C3×#5019 | 3 |