Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
172 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 76 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. (C31⋊C9)⋊C27 | C3 | semidirect |
| 3. (C31⋊C9)⋊C27 | C3 | semidirect |
| 4. (C31⋊C9)⋊C27 | C3 | semidirect |
| 6. #21419221 | C3 | semidirect |
| 7. #21419220 | C3 | semidirect |
| 8. C27×C31⋊C9 | C3 | semidirect |
| 84. C31 | #10624713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419296 | 3 |
| (C31⋊C9)⋊C27 | 3 |
| C32⋊(C31⋊C27) | 3 |
| #21419221 | 3 |
| #21419220 | 3 |
| C27×C31⋊C9 | 3 |
| C31×C32⋊C27 | 3 |
| #10624713 | 31 |