Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
144 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 28 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 |
|---|---|---|
| 2. #21419230 | C3 | semidirect |
| 3. C31⋊#6855 | C3 | semidirect |
| 4. C3×C31×#733 | C3 | semidirect |
| 46. C3×#733 | C31⋊C3 | semidirect |
| 65. C31 | #10624481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578900 | 3 |
| #21419230 | 3 |
| C31⋊#6855 | 3 |
| C3×C31×#733 | 3 |
| #10624481 | 31 |