Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
5964 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.
This group has 5964 conjugacy classes of subgroups — too many to draw. Only its 1123 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. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 2. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 3. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 4. C2×C33×C4⋊C4 | C2 | semidirect |
| 5. C2×#88859 | C2 | semidirect |
| 6. #11723936 | C2 | direct (N × H) |
| 15. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 16. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 18. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 19. C33×C4⋊C4 | C22 | semidirect |
| 20. #88859 | C22 | semidirect |
| 24. C2×C32×C4⋊C4 | D3 | semidirect |
| 33. C22×C3⋊(C3⋊D3) | D4 | semidirect |
| 37. C2×C33×C4 | D4 | semidirect |
| 57. C32×C4⋊C4 | C2×D3 | semidirect |
| 70. C2×C3⋊(C3⋊D3) | C2×D4 | semidirect |
| 72. C33×C4 | C2×D4 | semidirect |
| 77. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 90. C2×C32×C4 | D12 | semidirect |
| 99. C2×C33 | #121 | semidirect |
| 116. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 131. C32×C4 | C2×D12 | semidirect |
| 137. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 139. C33 | C2×#121 | semidirect |
| 150. C2×C3×C4 | C4⋊(C3⋊D3) | semidirect |
| 158. C2×C32 | #895 | semidirect |
| 175. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 190. C3×C4 | C2×C4⋊(C3⋊D3) | semidirect |
| 192. C32 | C2×#895 | semidirect |
| 208. C2×C4 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 211. C2×C3 | #64104 | semidirect |
| 231. C4 | C2×C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 232. C3 | C2×#64104 | semidirect |
| 235. C2 | #11723936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| #11723936 | 2 |
| C2×#64104 | 3 |