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. C3×#14578892 | C3 | semidirect |
| 4. #21419243 | C3 | semidirect |
| 5. #21419240 | C3 | semidirect |
| 6. #21419232 | C3 | semidirect |
| 7. C31×#6869 | C3 | semidirect |
| 57. #6869 | C31⋊C3 | semidirect |
| 77. C31 | #10624725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419391 | 3 |
| #21419372 | 3 |
| C3×#14578892 | 3 |
| #21419243 | 3 |
| #21419240 | 3 |
| #21419232 | 3 |
| C31×#6869 | 3 |
| #10624725 | 31 |