Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
380 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 4. #21419207 | C3 | direct (N × H) |
| 63. C3×C31 | #6858 | semidirect |
| 82. C31 | C3×#6858 | semidirect |
| 120. C3 | #21419207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| #21419207 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×#6858 | 31 |