Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1118 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|
| #21419437 | 3 |
| C31⋊H(5,𝔽3) | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| #21419397 | 3 |
| #21419396 | 3 |
| #21419395 | 3 |
| #21419394 | 3 |
| #21419393 | 3 |
| C3×#14578895 | 3 |
| C3×#14578893 | 3 |
| AΣL(1,𝔽27)×C31⋊C3 | 3 |
| C31×#6909 | 3 |
| #10624930 | 31 |