Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
936 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|---|
| 3. #21419409 | C3 | semidirect |
| 4. #21419408 | C3 | semidirect |
| 5. #21419407 | C3 | semidirect |
| 6. C3×#14578902 | C3 | semidirect |
| 7. #733×C31⋊C3 | C3 | semidirect |
| 8. C3×C31×#733 | C3 | semidirect |
| 74. C3×#733 | C31⋊C3 | semidirect |
| 100. C31 | #10624933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| C3×#14578912 | 3 |
| #21419409 | 3 |
| #21419408 | 3 |
| #21419407 | 3 |
| C3×#14578902 | 3 |
| #733×C31⋊C3 | 3 |
| C3×C31×#733 | 3 |
| #10624933 | 31 |