Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21419372 | C3 | semidirect |
| 3. #21419371 | C3 | semidirect |
| 4. C3×#14578891 | C3 | semidirect |
| 5. #21419244 | C3 | semidirect |
| 6. #21419243 | C3 | semidirect |
| 7. #21419242 | C3 | semidirect |
| 8. #21419231 | C3 | semidirect |
| 9. C31×#6872 | C3 | semidirect |
| 75. #6872 | C31⋊C3 | semidirect |
| 104. C31 | #10624725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419388 | 3 |
| #21419372 | 3 |
| #21419371 | 3 |
| C3×#14578891 | 3 |
| #21419244 | 3 |
| #21419243 | 3 |
| #21419242 | 3 |
| #21419231 | 3 |
| C31×#6872 | 3 |
| #10624725 | 31 |