Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2772 conjugacy classes of subgroups; only the 409 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 409 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×D4×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. C2×#88852 | C2 | semidirect |
| 4. #11723936 | C2 | semidirect |
| 5. C33×#102 | C2 | semidirect |
| 6. #11722190 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 16. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 18. C2×C33×C8 | C22 | semidirect |
| 19. C33×C4⋊C4 | C22 | semidirect |
| 22. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 28. C32×#102 | D3 | semidirect |
| 39. C33×D4 | D4 | semidirect |
| 48. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 63. C2×C32×C8 | C2×D3 | semidirect |
| 64. C32×C4⋊C4 | C2×D3 | semidirect |
| 82. C2×C3⋊(C3⋊D3) | D8 | semidirect |
| 91. C3×#102 | C3⋊D3 | semidirect |
| 102. C32×D4 | D12 | semidirect |
| 133. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 134. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 162. #102 | C3⋊(C3⋊D3) | semidirect |
| 164. C33 | #447 | semidirect |
| 173. C3×D4 | C4⋊(C3⋊D3) | semidirect |
| 206. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 207. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 227. C32 | #4773 | semidirect |
| 242. D4 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 275. C3 | #10592472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊(C3⋊D3) | 2 |
| C2×#88860 | 2 |
| C2×#88852 | 2 |
| #11723936 | 2 |
| C33×#102 | 2 |
| #11722190 | 2 |
| #11722179 | 2 |
| #10592472 | 3 |