Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
312 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. C3×#14578892 | C3 | semidirect |
| 3. C3×#14578892 | C3 | semidirect |
| 4. #21419231 | C3 | semidirect |
| 5. C3×C31×C27⋊C3 | C3 | semidirect |
| 87. C3×C27⋊C3 | C31⋊C3 | semidirect |
| 122. C31 | #10624694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| C3×#14578892 | 3 |
| #21419231 | 3 |
| C3×C31×C27⋊C3 | 3 |
| #10624694 | 31 |