Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
393 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 8. C2×#6188 | C4 | semidirect |
| 14. C2×C4×H(3,𝔽3) | C8 | semidirect |
| 17. C2×#1084 | C8 | semidirect |
| 85. H(3,𝔽3) | #336 | semidirect |
| 156. C2×C4 | #6188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6188 | 2 |
| C2×C4×#1084 | 2 |
| C3×#336 | 9 |