Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. #21419278 | C3 | semidirect |
| 5. #21419277 | C3 | semidirect |
| 6. #21419276 | C3 | semidirect |
| 7. #21419275 | C3 | semidirect |
| 8. #21419274 | C3 | semidirect |
| 9. C31×#6882 | C3 | semidirect |
| 70. #6882 | C31⋊C3 | direct (N × H) |
| 75. C31⋊C3 | #6882 | direct (N × H) |
| 91. C31 | C3×#6882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C31⋊C3 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| #21419278 | 3 |
| #21419277 | 3 |
| #21419276 | 3 |
| #21419275 | 3 |
| #21419274 | 3 |
| C31×#6882 | 3 |
| C3×#6882 | 31 |