Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
302 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 1. #21419310 | C3 | semidirect |
| 3. C32⋊C9×C31⋊C3 | C3 | semidirect |
| 4. C32⋊C9×C31⋊C3 | C3 | semidirect |
| 5. #21419211 | C3 | semidirect |
| 6. #21419211 | C3 | semidirect |
| 7. #21419210 | C3 | semidirect |
| 8. #21419209 | C3 | semidirect |
| 9. C31×#6859 | C3 | semidirect |
| 96. #6859 | C31⋊C3 | semidirect |
| 128. C31 | #10624598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419310 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419211 | 3 |
| #21419210 | 3 |
| #21419209 | 3 |
| C31×#6859 | 3 |
| #10624598 | 31 |