Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1886 conjugacy classes of subgroups; only the 488 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 488 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×C92 | C2 | semidirect |
| 2. C2×#10619673 | C2 | semidirect |
| 3. #13047416 | C2 | direct (N × H) |
| 4. C2×C4⋊(C9⋊D9) | C2 | semidirect |
| 5. C2×C4×C9⋊D9 | C2 | semidirect |
| 6. C2×#10619651 | C2 | semidirect |
| 12. C2×C4×C92 | C22 | semidirect |
| 13. #10619673 | C22 | semidirect |
| 15. C4⋊(C9⋊D9) | C22 | semidirect |
| 16. C4×C9⋊D9 | C22 | semidirect |
| 17. #10619651 | C22 | semidirect |
| 45. C2×C92 | #41 | semidirect |
| 54. C22×C4×C9 | D9 | semidirect |
| 69. C92 | C2×#41 | semidirect |
| 84. C2×C4×C9 | C2×D9 | semidirect |
| 133. C2×C9 | #3697 | semidirect |
| 141. C22×C4 | C9⋊D9 | semidirect |
| 151. C9 | C2×#3697 | semidirect |
| 161. C2×C4 | C2×C9⋊D9 | semidirect |
| 177. C2 | #13047416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C92 | 2 |
| C2×#10619673 | 2 |
| #13047416 | 2 |
| C2×C4⋊(C9⋊D9) | 2 |
| C2×C4×C9⋊D9 | 2 |
| C2×#10619651 | 2 |
| C2×#88736 | 3 |