Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1328 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 313 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419319 | 3 |
| #21419318 | 3 |
| #21419317 | 3 |
| #21419316 | 3 |
| #21419315 | 3 |
| #21419314 | 3 |
| #21419313 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| C31×C9⋊H(3,𝔽3) | 3 |
| C3×C9⋊H(3,𝔽3) | 31 |