Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 212 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 |
| 3. C3×#14578887 | C3 | semidirect |
| 4. #21419279 | C3 | direct (N × H) |
| 5. C3×C31×#733 | C3 | semidirect |
| 10. #14578902 | C32 | semidirect |
| 14. #14578887 | C32 | semidirect |
| 18. C31×#733 | C32 | semidirect |
| 48. C3×#733 | C31⋊C3 | semidirect |
| 54. C3×C31 | #6883 | semidirect |
| 65. #733 | C3×C31⋊C3 | semidirect |
| 70. C31 | C3×#6883 | semidirect |
| 101. C3 | #21419279 | 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×#14578887 | 3 |
| #21419279 | 3 |
| C3×C31×#733 | 3 |
| C3×#6883 | 31 |