Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
196 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 22 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. #21419312 | C3 | semidirect |
| 3. #21419226 | C3 | semidirect |
| 4. C31×#6866 | C3 | semidirect |
| 50. #6866 | C31⋊C3 | semidirect |
| 65. C31 | #10624475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419312 | 3 |
| #21419308 | 3 |
| #21419226 | 3 |
| C31×#6866 | 3 |
| #10624475 | 31 |