Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×C16×H(3,𝔽3) | C2 | semidirect |
| 3. #11720552 | C2 | semidirect |
| 13. C2×C32×C16 | D3 | semidirect |
| 75. C2×C16 | #272 | semidirect |
| 77. H(3,𝔽3) | #359 | semidirect |
| 114. C32 | #4510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721779 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| #11720552 | 2 |
| C3×#4510 | 3 |