Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
423 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 423 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720785 | C2 | semidirect |
| 4. C4⋊#6188 | C2 | semidirect |
| 23. C4×#272 | C8 | semidirect |
| 41. C4×H(3,𝔽3) | C2×C8 | semidirect |
| 43. #1084 | C2×C8 | semidirect |
| 66. #272 | C4⋊C8 | semidirect |
| 98. H(3,𝔽3) | C2×C4⋊C8 | semidirect |
| 187. C4 | #88626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88626 | 2 |
| C42×#272 | 2 |
| #11720785 | 2 |
| C4⋊#6188 | 2 |
| C2×C3×C4⋊C8 | 9 |