Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
379 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 379 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11720704 | C2 | direct (N × H) |
| 6. C2×#6188 | C4 | semidirect |
| 18. #6188 | C2×C4 | semidirect |
| 47. C2×H(3,𝔽3) | #107 | semidirect |
| 74. H(3,𝔽3) | C2×#107 | semidirect |
| 146. C2 | #11720704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6188 | 2 |
| C2×#88449 | 2 |
| #11720704 | 2 |
| C2×#818 | 9 |