Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
356 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 5. #21419208 | C3 | semidirect |
| 6. #21419207 | C3 | semidirect |
| 7. #21419206 | C3 | semidirect |
| 8. #21419205 | C3 | semidirect |
| 9. C31×#6858 | C3 | semidirect |
| 91. #6858 | C31⋊C3 | semidirect |
| 122. C31 | #10624592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| #21419310 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419208 | 3 |
| #21419207 | 3 |
| #21419206 | 3 |
| #21419205 | 3 |
| C31×#6858 | 3 |
| #10624592 | 31 |