Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
539 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 539 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 |
|---|---|---|
| 1. C2×#88529 | C2 | semidirect |
| 2. C2×C16×H(3,𝔽3) | C2 | semidirect |
| 3. #11720512 | C2 | direct (N × H) |
| 8. #88529 | C22 | semidirect |
| 9. C16×H(3,𝔽3) | C22 | semidirect |
| 11. C2×C32×C16 | D3 | semidirect |
| 25. C32×C16 | C2×D3 | semidirect |
| 44. C2×H(3,𝔽3) | D16 | semidirect |
| 64. C2×C16 | #272 | semidirect |
| 65. H(3,𝔽3) | C2×D16 | semidirect |
| 78. C2×C32 | D48 | semidirect |
| 85. C16 | C2×#272 | semidirect |
| 96. C32 | C2×D48 | semidirect |
| 117. C2 | #11720512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| #11720512 | 2 |
| C2×C3×D48 | 3 |