Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
274 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 17. C31×#733 | C9 | semidirect |
| 44. C31⋊C9 | #733 | direct (N × H) |
| 59. #733 | C31⋊C9 | direct (N × H) |
| 67. C31 | C9×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C31⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| #21419230 | 3 |
| C3×C31×#733 | 3 |
| C9×#733 | 31 |