Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #11721779 | C2 | semidirect |
| 2. C2×C16×H(3,𝔽3) | C2 | semidirect |
| 3. #11720514 | C2 | semidirect |
| 4. #11720513 | C2 | semidirect |
| 5. #11720512 | C2 | semidirect |
| 15. C2×C32×C16 | D3 | semidirect |
| 84. C2×C16 | #272 | semidirect |
| 85. H(3,𝔽3) | #508 | semidirect |
| 120. C32 | #4904 | 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 |
| #11720514 | 2 |
| #11720513 | 2 |
| #11720512 | 2 |
| C3×#4904 | 3 |