Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 6. C42×H(3,𝔽3) | C4 | semidirect |
| 7. C4×#1084 | C4 | semidirect |
| 23. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 24. #1084 | C4⋊C4 | semidirect |
| 52. H(3,𝔽3) | #384 | semidirect |
| 71. C42 | #1088 | semidirect |
| 101. C4 | C4⋊#1088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1088 | 2 |
| C42×#272 | 2 |
| C3×#384 | 9 |