Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 515 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×C8 | C2 | semidirect |
| 2. #11723971 | C2 | semidirect |
| 3. C2×#88852 | C2 | semidirect |
| 4. #11722191 | C2 | semidirect |
| 5. #11722188 | C2 | semidirect |
| 16. C22×C32×C8 | D3 | semidirect |
| 32. C33×C8 | D4 | semidirect |
| 45. C22×C33 | D8 | semidirect |
| 54. C22×C3×C8 | C3⋊D3 | semidirect |
| 70. C32×C8 | #67 | semidirect |
| 88. C22×C32 | D24 | semidirect |
| 98. C22×C8 | C3⋊(C3⋊D3) | semidirect |
| 102. C33 | #466 | semidirect |
| 114. C3×C8 | #638 | semidirect |
| 131. C22×C3 | #3745 | semidirect |
| 140. C32 | #5115 | semidirect |
| 152. C8 | #6312 | semidirect |
| 163. C22 | #88852 | semidirect |
| 169. C3 | #10592814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C8 | 2 |
| #11723971 | 2 |
| C2×#88852 | 2 |
| #11722191 | 2 |
| #11722188 | 2 |
| #10592814 | 3 |