Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
342 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 81 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. #3676⋊C9 | C2 | semidirect |
| 5. C23×C9⋊C9 | C4 | semidirect |
| 8. C2×C4×C9⋊C9 | C4 | semidirect |
| 24. #63393 | C9 | semidirect |
| 50. #3676 | C2×C9 | semidirect |
| 73. C9⋊C9 | #99 | semidirect |
| 85. C23×C9 | C4×C9 | semidirect |
| 95. C2×C4×C9 | C4×C9 | semidirect |
| 211. C9 | C9×#99 | semidirect |
| 212. C23 | Dic9⋊C9 | semidirect |
| 216. C2×C4 | Dic9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C9⋊C9 | 2 |
| #3676⋊C9 | 2 |
| C9×#834 | 3 |
| C3×#63393 | 3 |