Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2972 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 2972 conjugacy classes of subgroups — too many to draw. Only its 452 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×C3×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C22×C32×C3⋊C8 | C2 | semidirect |
| 4. C2×#88791 | C2 | direct (N × H) |
| 11. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 13. C2×C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. C2×C32×C3⋊C8 | C22 | semidirect |
| 15. #88791 | C22 | direct (N × H) |
| 19. C22×C4⋊(C3⋊D3) | D3 | semidirect |
| 23. C22×C3×C3⋊C8 | D3 | semidirect |
| 33. C4⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 35. C3×C4⋊(C3⋊D3) | C23 | semidirect |
| 36. C32×C3⋊C8 | C23 | semidirect |
| 54. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 59. C2×C3×C3⋊C8 | C2×D3 | semidirect |
| 61. C22×C33 | D8 | semidirect |
| 76. C22×C3⋊C8 | C3⋊D3 | semidirect |
| 104. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 108. C3×C3⋊C8 | C22×D3 | semidirect |
| 110. C2×C33 | C2×D8 | semidirect |
| 134. C2×C3⋊C8 | C2×C3⋊D3 | semidirect |
| 138. C22×C32 | D24 | semidirect |
| 139. C22×C32 | #213 | semidirect |
| 162. C33 | C22×D8 | semidirect |
| 193. C3⋊C8 | C22×C3⋊D3 | semidirect |
| 196. C2×C32 | C2×D24 | semidirect |
| 197. C2×C32 | C2×#213 | semidirect |
| 218. C22×C3 | #3714 | semidirect |
| 219. C22×C3 | #3745 | semidirect |
| 237. C32 | C22×D24 | semidirect |
| 238. C32 | C22×#213 | semidirect |
| 254. C2×C3 | C2×#3714 | semidirect |
| 255. C2×C3 | C2×#3745 | semidirect |
| 266. C22 | #88791 | direct (N × H) |
| 271. C3 | C22×#3714 | semidirect |
| 272. C3 | C22×#3745 | semidirect |
| 275. C2 | C2×#88791 | 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×C3×C4⋊(C3⋊D3) | 2 |
| C22×C32×C3⋊C8 | 2 |
| C2×#88791 | 2 |
| C22×#3745 | 3 |
| C22×#3714 | 3 |