Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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. C9×#3667 | C2 | semidirect |
| 20. #63391 | C9 | direct (N × H) |
| 43. #3667 | C2×C9 | semidirect |
| 58. C92 | #100 | semidirect |
| 169. C9 | #63391 | direct (N × H) |
| 170. C9 | C9×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C92 | 2 |
| C9×#3667 | 2 |
| C9×#833 | 3 |
| C3×#63391 | 3 |