Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1092 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 2. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 3. C32×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #11722021 | C2 | semidirect |
| 23. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 25. C3×C4⋊(C3⋊C8) | D3 | semidirect |
| 89. C4⋊(C3⋊C8) | C3⋊D3 | semidirect |
| 195. C33 | #432 | semidirect |
| 288. C32 | #4835 | semidirect |
| 289. C32 | #4835 | semidirect |
| 327. C3 | #10590260 | semidirect |
| 328. C3 | #10592534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊(C3⋊D3) | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722024 | 2 |
| #11722021 | 2 |
| #10592534 | 3 |
| #10590260 | 3 |