Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 407 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. C2×C33×Q16 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 5. #11722188 | C2 | semidirect |
| 16. C2×C32×Q16 | D3 | semidirect |
| 45. C2×C3⋊(C3⋊D3) | Q16 | semidirect |
| 51. C2×C3×Q16 | C3⋊D3 | semidirect |
| 90. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 95. C33 | #467 | semidirect |
| 129. C32 | #5188 | semidirect |
| 154. C3 | #10592887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| #11723987 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11722205 | 2 |
| #11722188 | 2 |
| #10592887 | 3 |