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. 3−1+2×C31⋊C9 | C3 | semidirect |
| 3. #21419293 | C3 | semidirect |
| 4. C31⋊#6862 | C3 | semidirect |
| 5. #21419215 | C3 | semidirect |
| 7. #21419205 | C3 | semidirect |
| 8. #21419205 | C3 | semidirect |
| 88. C31 | #10624587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C31⋊C9 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419293 | 3 |
| C31⋊#6862 | 3 |
| #21419215 | 3 |
| #21419209 | 3 |
| #21419205 | 3 |
| C31×#6857 | 3 |
| #10624587 | 31 |