Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
250 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 19. #14578901 | C9 | semidirect |
| 134. C31 | #10624723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578901 | 3 |
| #21419306 | 3 |
| 3−1+2×C31⋊C9 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| #21419239 | 3 |
| #21419238 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419236 | 3 |
| #21419229 | 3 |
| C31×3−1+2⋊C9 | 3 |
| #10624723 | 31 |