Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
680 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×#11719689 | C3 | semidirect |
| 3. #21419204 | C3 | direct (N × H) |
| 4. C3×C31×C32⋊C9 | C3 | semidirect |
| 8. C3×#11719689 | C32 | semidirect |
| 16. C31×C32⋊C9 | C32 | semidirect |
| 55. C3×C32⋊C9 | C31⋊C3 | semidirect |
| 59. C3×C31 | #6857 | semidirect |
| 75. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 76. C31 | C3×#6857 | semidirect |
| 115. C3 | #21419204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| #21419204 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×#6857 | 31 |