Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1736 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×#88851 | C2 | semidirect |
| 2. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. #11723938 | C2 | semidirect |
| 5. C33×#106 | C2 | semidirect |
| 6. #11722180 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 26. C32×#106 | D3 | semidirect |
| 43. C33×C8 | D4 | semidirect |
| 65. C2×C3⋊(C3⋊D3) | SD16 | semidirect |
| 76. C3×#106 | C3⋊D3 | semidirect |
| 93. C32×C8 | D12 | semidirect |
| 131. #106 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #465 | semidirect |
| 149. C3×C8 | C4⋊(C3⋊D3) | semidirect |
| 182. C32 | #4864 | semidirect |
| 198. C8 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 217. C3 | #10592563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88851 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723938 | 2 |
| #11723936 | 2 |
| C33×#106 | 2 |
| #11722180 | 2 |
| #11722179 | 2 |
| #10592563 | 3 |