Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1960 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1960 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. C33×C4×D4 | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. #11723915 | C2 | semidirect |
| 4. #11722179 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 17. C32×C4×D4 | D3 | semidirect |
| 25. C33×D4 | D4 | semidirect |
| 56. C33×C4 | D8 | semidirect |
| 59. C3×C4×D4 | C3⋊D3 | semidirect |
| 67. C32×D4 | D12 | semidirect |
| 103. C32×C4 | #213 | semidirect |
| 108. C4×D4 | C3⋊(C3⋊D3) | semidirect |
| 111. C33 | #459 | semidirect |
| 115. C3×D4 | C4⋊(C3⋊D3) | semidirect |
| 150. C3×C4 | #3753 | semidirect |
| 153. C32 | #5015 | semidirect |
| 161. D4 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 182. C4 | #88860 | semidirect |
| 185. C3 | #10592714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C2×#88860 | 2 |
| #11723915 | 2 |
| #11722179 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592714 | 3 |