Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2632 conjugacy classes of subgroups; only the 409 normal subgroups are shown.
This group has 2632 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 |
|---|---|---|
| 2. C2×#88861 | C2 | semidirect |
| 3. C2×#88851 | C2 | semidirect |
| 4. #11723938 | C2 | semidirect |
| 5. C33×#102 | C2 | semidirect |
| 6. #11722190 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 16. C2×#6308 | C22 | semidirect |
| 17. C2×C33×C8 | C22 | semidirect |
| 18. C33×C4⋊C4 | C22 | semidirect |
| 22. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 28. C32×#102 | D3 | semidirect |
| 61. C2×C32×C8 | C2×D3 | semidirect |
| 62. C32×C4⋊C4 | C2×D3 | semidirect |
| 78. C2×C3⋊(C3⋊D3) | SD16 | semidirect |
| 88. C3×#102 | C3⋊D3 | semidirect |
| 127. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 128. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 155. #102 | C3⋊(C3⋊D3) | semidirect |
| 157. C33 | #450 | semidirect |
| 196. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 198. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 216. C32 | #4776 | semidirect |
| 260. C3 | #10592475 | 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×#88861 | 2 |
| C2×#88851 | 2 |
| #11723938 | 2 |
| C33×#102 | 2 |
| #11722190 | 2 |
| #11722179 | 2 |
| #10592475 | 3 |