Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2828 conjugacy classes of subgroups; only the 741 normal subgroups are shown.
This group has 2828 conjugacy classes of subgroups — too many to draw. Only its 741 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. C22×C33×Q8 | C2 | semidirect |
| 3. #11722201 | C2 | semidirect |
| 10. C22×C32×Q8 | D3 | semidirect |
| 16. C22×C3⋊(C3⋊D3) | Q8 | semidirect |
| 36. C22×C3×Q8 | C3⋊D3 | semidirect |
| 66. C22×Q8 | C3⋊(C3⋊D3) | semidirect |
| 69. C33 | #393 | semidirect |
| 96. C32 | #5231 | semidirect |
| 118. C3 | #10592930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×#88859 | 2 |
| #11722201 | 2 |
| #10592930 | 3 |