Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 405 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. #11722187 | C2 | semidirect |
| 16. C2×C32×Q16 | D3 | semidirect |
| 50. C2×C3×Q16 | C3⋊D3 | semidirect |
| 87. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 92. C33 | #470 | semidirect |
| 124. C32 | #5189 | semidirect |
| 147. C3 | #10592888 | 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×#88850 | 2 |
| #11722205 | 2 |
| #11722187 | 2 |
| #10592888 | 3 |