Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
363 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#88386 | C2 | semidirect |
| 13. C2×C32×C16 | D3 | semidirect |
| 35. C2×#272 | C16 | semidirect |
| 81. C2×C16 | #272 | semidirect |
| 82. H(3,𝔽3) | C22⋊C16 | semidirect |
| 124. C32 | (C2×D3)⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| C2×#88386 | 2 |
| C3×(C2×D3)⋊C16 | 3 |