Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 847 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 847 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 |
|---|---|---|
| 7. C2×C33×C8 | C4 | semidirect |
| 9. C4⋊(C3⋊(C3⋊Dic3)) | C4 | semidirect |
| 25. C2×C32×C8 | Dic3 | semidirect |
| 57. C2×C3×C8 | C3⋊Dic3 | semidirect |
| 71. C33 | #340 | semidirect |
| 89. C2×C8 | C3⋊(C3⋊Dic3) | semidirect |
| 101. C32 | #4551 | semidirect |
| 125. C3 | #10589417 | 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×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #10589417 | 3 |