Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
236 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 236 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. #21419336 | C3 | semidirect |
| 2. #21419317 | C3 | semidirect |
| 3. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 4. #21419216 | C3 | semidirect |
| 5. #21419216 | C3 | semidirect |
| 6. #21419215 | C3 | semidirect |
| 7. #21419211 | C3 | semidirect |
| 8. #21419211 | C3 | semidirect |
| 9. #21419209 | C3 | semidirect |
| 10. #21419201 | C3 | semidirect |
| 11. #21419200 | C3 | semidirect |
| 12. #21419200 | C3 | semidirect |
| 13. C9×H(3,𝔽3)×C31 | C3 | semidirect |
| 95. C9×H(3,𝔽3) | C31⋊C3 | semidirect |
| 138. C31 | #10624622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419336 | 3 |
| #21419317 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| #21419216 | 3 |
| #21419215 | 3 |
| #21419211 | 3 |
| #21419209 | 3 |
| #21419201 | 3 |
| #21419200 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624622 | 31 |