Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
312 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 88 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. C27⋊C3×C31⋊C3 | C3 | semidirect |
| 3. #21419232 | C3 | semidirect |
| 4. #21419231 | C3 | semidirect |
| 5. C31×#6869 | C3 | semidirect |
| 64. #6869 | C31⋊C3 | semidirect |
| 86. 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 |
| C27⋊C3×C31⋊C3 | 3 |
| #21419232 | 3 |
| #21419231 | 3 |
| C31×#6869 | 3 |
| #10624694 | 31 |