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×C33×D8 | C2 | semidirect |
| 3. #11723979 | C2 | semidirect |
| 4. C2×#88860 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722190 | C2 | semidirect |
| 11. C2×C33×D4 | C22 | semidirect |
| 19. C2×C33×C8 | C22 | semidirect |
| 22. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 23. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 25. C2×C32×D8 | D3 | semidirect |
| 41. C33×D4 | D4 | semidirect |
| 48. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 56. C2×C32×D4 | C2×D3 | semidirect |
| 64. C2×C32×C8 | C2×D3 | semidirect |
| 82. C2×C3⋊(C3⋊D3) | D8 | semidirect |
| 88. C2×C3×D8 | C3⋊D3 | semidirect |
| 104. C32×D4 | #67 | semidirect |
| 126. C2×C3×D4 | C2×C3⋊D3 | semidirect |
| 134. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 159. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 164. C33 | #447 | semidirect |
| 175. C3×D4 | #638 | semidirect |
| 201. C2×D4 | C2×C3⋊(C3⋊D3) | semidirect |
| 206. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 227. C32 | #5156 | semidirect |
| 242. D4 | #6312 | semidirect |
| 275. C3 | #10592855 | 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×C33×D8 | 2 |
| #11723979 | 2 |
| C2×#88860 | 2 |
| #11722202 | 2 |
| #11722191 | 2 |
| #11722190 | 2 |
| #10592855 | 3 |