Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
782 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 264 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×#10619651 | C2 | semidirect |
| 3. #13046805 | C2 | direct (N × H) |
| 4. C2×C9⋊(C9⋊C8) | C2 | semidirect |
| 12. #10619651 | C22 | semidirect |
| 13. C9⋊(C9⋊C8) | C22 | semidirect |
| 35. C2×C92 | SD16 | semidirect |
| 52. C92 | C2×SD16 | semidirect |
| 102. C2×C9 | #3672 | semidirect |
| 115. C9 | C2×#3672 | semidirect |
| 135. C2 | #13046805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C92 | 2 |
| C2×#10619651 | 2 |
| #13046805 | 2 |
| C2×C9⋊(C9⋊C8) | 2 |
| C2×#88543 | 3 |