Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1052 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|---|
| 3. C3×#14578902 | C3 | semidirect |
| 4. C3×#14578901 | C3 | semidirect |
| 5. #733×C31⋊C3 | C3 | direct (N × H) |
| 6. C3×C31×#733 | C3 | semidirect |
| 20. #14578902 | C32 | semidirect |
| 21. #14578901 | C32 | semidirect |
| 24. C31×#733 | C32 | semidirect |
| 59. C3×C31⋊C3 | #733 | direct (N × H) |
| 72. C3×#733 | C31⋊C3 | direct (N × H) |
| 75. C3×C31 | C3×#733 | semidirect |
| 79. C31⋊C3 | C3×#733 | direct (N × H) |
| 97. #733 | C3×C31⋊C3 | direct (N × H) |
| 98. C31 | C32×#733 | semidirect |
| 145. C3 | #733×C31⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| C32×C9×C31⋊C3 | 3 |
| C3×#14578902 | 3 |
| C3×#14578901 | 3 |
| #733×C31⋊C3 | 3 |
| C3×C31×#733 | 3 |
| C32×#733 | 31 |