Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
427 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 427 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 9. C9×H(5,𝔽2) | C9 | semidirect |
| 37. C23×C9 | C22⋊C9 | semidirect |
| 39. Q8×C9 | C22⋊C9 | semidirect |
| 59. H(5,𝔽2) | C9⋊C9 | semidirect |
| 89. C9 | #63703 | semidirect |
| 91. C23 | C9⋊(C22⋊C9) | semidirect |
| 92. Q8 | C9⋊(C22⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 3 |
| C3×#63703 | 3 |
| C2×C9⋊(C22⋊C9) | 4 |
| C9⋊(Q8⋊C9) | 4 |