Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1708 conjugacy classes of subgroups; only the 523 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 523 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. C33×C4×Q8 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 6. #11722178 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 16. #88862 | C4 | direct (N × H) |
| 21. C32×C4×Q8 | D3 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 62. C33×C4 | SD16 | semidirect |
| 66. C3×C4×Q8 | C3⋊D3 | semidirect |
| 75. C32×Q8 | C4×D3 | semidirect |
| 111. C32×C4 | #215 | semidirect |
| 116. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 122. C33 | C4×SD16 | semidirect |
| 125. C3×Q8 | C4×C3⋊D3 | semidirect |
| 160. C3×C4 | #3755 | semidirect |
| 164. C32 | C4×#215 | semidirect |
| 167. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 191. C4 | #88862 | direct (N × H) |
| 194. C3 | C4×#3755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| C2×#88862 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11722205 | 2 |
| #11722179 | 2 |
| #11722178 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C4×#3755 | 3 |