Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
220 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 52 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. #21419306 | C3 | semidirect |
| 2. #21419306 | C3 | semidirect |
| 4. #21419293 | C3 | semidirect |
| 5. C31⋊#6862 | C3 | semidirect |
| 6. #21419216 | C3 | semidirect |
| 8. #21419208 | C3 | semidirect |
| 9. #21419207 | C3 | semidirect |
| 10. #21419206 | C3 | semidirect |
| 11. #21419206 | C3 | semidirect |
| 118. C31 | #10624587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419306 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419293 | 3 |
| C31⋊#6862 | 3 |
| #21419216 | 3 |
| #21419209 | 3 |
| #21419208 | 3 |
| #21419207 | 3 |
| #21419206 | 3 |
| #21419203 | 3 |
| C31×#6859 | 3 |
| #10624587 | 31 |