Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 129 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×C3×C9×C16 | C2 | semidirect |
| 3. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 17. C2×C9×C16 | D3 | semidirect |
| 46. C2×C3⋊D9 | C16 | semidirect |
| 52. C2×C3×C16 | D9 | semidirect |
| 107. C2×C16 | C3⋊D9 | semidirect |
| 108. C3×C9 | C22⋊C16 | semidirect |
| 155. C9 | (C2×D3)⋊C16 | semidirect |
| 179. C3 | (C2×D9)⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| C2×C3×C9×C16 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #10589373 | 3 |
| (C2×D9)⋊C16 | 3 |