Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
451 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. C4⋊#6180 | C2 | semidirect |
| 3. C4×#6180 | C2 | semidirect |
| 17. D4×H(3,𝔽3) | C8 | semidirect |
| 53. C32×D4 | C3⋊C8 | semidirect |
| 94. H(3,𝔽3) | D4⋊C8 | semidirect |
| 148. C32 | D4⋊(C3⋊C8) | semidirect |
| 151. D4 | #6180 | 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 |
| C4⋊#6180 | 2 |
| C4×#6180 | 2 |
| C3×D4⋊(C3⋊C8) | 3 |