Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
591 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11720304 | C2 | direct (N × H) |
| 23. C2×#1084 | C8 | semidirect |
| 51. #1084 | C2×C8 | semidirect |
| 81. C2×H(3,𝔽3) | C4⋊C8 | semidirect |
| 127. H(3,𝔽3) | C2×C4⋊C8 | semidirect |
| 162. C2×C32 | Dic3⋊C8 | semidirect |
| 201. C32 | C2×Dic3⋊C8 | semidirect |
| 236. C2 | #11720304 | 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 |
| C22×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #11720304 | 2 |
| C2×Dic3⋊(C3⋊C8) | 3 |