Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
924 conjugacy classes of subgroups; only the 507 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 507 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⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 26. C22×C33 | C16 | semidirect |
| 52. C22×C32 | C3⋊C16 | semidirect |
| 59. C33 | C22⋊C16 | semidirect |
| 78. C22×C3 | C3⋊(C3⋊C16) | semidirect |
| 83. C32 | #4549 | semidirect |
| 97. C22 | C3⋊(C3⋊(C3⋊C16)) | semidirect |
| 102. C3 | #10589415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C8 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| #10589415 | 3 |