Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1792 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 461 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×#88851 | C2 | semidirect |
| 3. C4×#6308 | C2 | semidirect |
| 4. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722191 | C2 | semidirect |
| 20. C32×C4⋊C8 | D3 | semidirect |
| 33. #6308 | D4 | semidirect |
| 51. C33×C4 | SD16 | semidirect |
| 59. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 94. C32×C4 | #204 | semidirect |
| 102. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 104. C33 | #460 | semidirect |
| 137. C3×C4 | #3744 | semidirect |
| 142. C32 | #4848 | semidirect |
| 167. C4 | #88851 | semidirect |
| 170. C3 | #10592547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88851 | 2 |
| #11723915 | 2 |
| C4×#6308 | 2 |
| C33×C4⋊C8 | 2 |
| #11722191 | 2 |
| #10592547 | 3 |