Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
260 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 5. #21419216 | C3 | semidirect |
| 6. #21419216 | C3 | semidirect |
| 7. #21419215 | C3 | semidirect |
| 8. #21419214 | C3 | semidirect |
| 9. C31×#6861 | C3 | semidirect |
| 86. #6861 | C31⋊C3 | semidirect |
| 116. C31 | #10624600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419310 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419216 | 3 |
| #21419215 | 3 |
| #21419214 | 3 |
| C31×#6861 | 3 |
| #10624600 | 31 |