Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
224 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×#14578902 | C3 | semidirect |
| 2. C3×#14578900 | C3 | semidirect |
| 3. C3×#14578886 | C3 | semidirect |
| 4. #21419270 | C3 | direct (N × H) |
| 5. C3×C31×#732 | C3 | semidirect |
| 10. #14578902 | C32 | semidirect |
| 12. #14578900 | C32 | semidirect |
| 14. #14578886 | C32 | semidirect |
| 18. C31×#732 | C32 | semidirect |
| 50. C3×#732 | C31⋊C3 | semidirect |
| 56. C3×C31 | #6881 | semidirect |
| 69. #732 | C3×C31⋊C3 | semidirect |
| 72. C31 | C3×#6881 | semidirect |
| 105. C3 | #21419270 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578902 | 3 |
| C3×#14578900 | 3 |
| C3×#14578886 | 3 |
| #21419270 | 3 |
| C3×C31×#732 | 3 |
| C3×#6881 | 31 |