Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
458 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 9. C3×H(3,𝔽3)×C31 | C9 | semidirect |
| 60. C3×H(3,𝔽3) | C31⋊C9 | semidirect |
| 63. C31 | #10624449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C31⋊C9) | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| #10624449 | 31 |