Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
220 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. C9×#11719689 | C3 | semidirect |
| 3. C31⋊#6862 | C3 | semidirect |
| 4. #21419215 | C3 | semidirect |
| 6. #21419208 | C3 | semidirect |
| 7. #21419206 | C3 | semidirect |
| 9. C31×#6887 | C3 | semidirect |
| 59. #6887 | C31⋊C3 | semidirect |
| 86. C31 | #10624587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C31⋊#6862 | 3 |
| #21419215 | 3 |
| #21419211 | 3 |
| #21419208 | 3 |
| #21419206 | 3 |
| #21419204 | 3 |
| C31×#6887 | 3 |
| #10624587 | 31 |