Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
451 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. H(3,𝔽3)×Q32 | C2 | semidirect |
| 3. #11720570 | C2 | semidirect |
| 4. #11720514 | C2 | semidirect |
| 15. C32×Q32 | D3 | semidirect |
| 59. #272 | Q32 | direct (N × H) |
| 82. Q32 | #272 | direct (N × H) |
| 84. H(3,𝔽3) | C2×Q32 | semidirect |
| 118. C32 | D3×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#272 | 2 |
| H(3,𝔽3)×Q32 | 2 |
| #11720570 | 2 |
| #11720514 | 2 |
| C16×#272 | 2 |
| C3×D3×Q32 | 3 |