Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
435 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11720783 | C2 | semidirect |
| 7. #88626 | C4 | semidirect |
| 19. #6188 | C2×C4 | semidirect |
| 47. #272 | #97 | semidirect |
| 70. H(3,𝔽3) | C2×#97 | 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 |
| #11720783 | 2 |
| C2×C3×#97 | 9 |