Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1388 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 1388 conjugacy classes of subgroups — too many to draw. Only its 160 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×#89026 | C2 | semidirect |
| 2. C2×C32×D24 | C2 | semidirect |
| 3. #11723531 | C2 | semidirect |
| 4. C2×#88789 | C2 | semidirect |
| 5. #11722190 | C2 | semidirect |
| 6. C3×#63648 | C2 | semidirect |
| 7. #11722031 | C2 | semidirect |
| 14. C2×C32×D12 | C22 | semidirect |
| 19. C2×C33×C8 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 21. C3×C4⋊(C3⋊Dic3) | C22 | semidirect |
| 30. C2×C3×D24 | D3 | semidirect |
| 34. #63648 | D3 | semidirect |
| 53. C3×C4⋊(C3⋊D3) | D4 | semidirect |
| 57. C32×D12 | D4 | semidirect |
| 78. C2×C3×D12 | C2×D3 | semidirect |
| 85. C2×C32×C8 | C2×D3 | semidirect |
| 86. C2×C32×C8 | C2×D3 | semidirect |
| 89. C4⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 100. C2×C3⋊(C3⋊D3) | D8 | semidirect |
| 121. C2×D24 | C3⋊D3 | semidirect |
| 159. C4⋊(C3⋊D3) | D12 | semidirect |
| 172. C3×D12 | #67 | semidirect |
| 204. C2×D12 | C2×C3⋊D3 | semidirect |
| 210. C2×C3×C8 | D32 | semidirect |
| 211. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 272. C33 | #447 | semidirect |
| 311. D12 | #638 | semidirect |
| 354. C2×C8 | D3×C3⋊D3 | semidirect |
| 401. C32 | #4773 | semidirect |
| 402. C32 | #5156 | semidirect |
| 462. C3 | #10590945 | semidirect |
| 463. C3 | #10592855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89026 | 2 |
| C2×C32×D24 | 2 |
| #11723531 | 2 |
| C2×#88789 | 2 |
| #11722190 | 2 |
| C3×#63648 | 2 |
| #11722031 | 2 |
| #10592855 | 3 |
| #10590945 | 3 |