Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
520 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 3. #13049781 | C2 | direct (N × H) |
| 5. C2×#66472 | C4 | semidirect |
| 7. #10620198 | C4 | semidirect |
| 19. #66472 | C2×C4 | semidirect |
| 29. C2×C34 | C4⋊C4 | semidirect |
| 30. C3⋊(C3⋊(C3⋊D3)) | C4⋊C4 | semidirect |
| 32. C32×C3⋊D3 | C4⋊C4 | semidirect |
| 33. C32×C3⋊D3 | C4⋊C4 | semidirect |
| 59. C34 | C2×C4⋊C4 | semidirect |
| 143. C2×C32 | #3773 | semidirect |
| 144. C2×C32 | #3777 | semidirect |
| 159. C3⋊D3 | #3773 | semidirect |
| 160. C3⋊D3 | #3777 | semidirect |
| 192. C32 | C2×#3773 | semidirect |
| 193. C32 | C2×#3777 | semidirect |
| 236. C2 | #13049781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620198 | 2 |
| C2×#10620197 | 2 |
| #13049781 | 2 |
| C2×#3777 | 9 |
| C2×#3773 | 9 |