Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
297 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 109 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. C16×H(3,𝔽3) | C4 | semidirect |
| 9. #88386 | C4 | semidirect |
| 23. C32×C16 | Dic3 | semidirect |
| 60. H(3,𝔽3) | #346 | semidirect |
| 77. C16 | #1084 | semidirect |
| 86. C32 | #4502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×H(3,𝔽3) | 2 |
| C8×#1084 | 2 |
| C2×#88386 | 2 |
| C3×#4502 | 3 |