Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 19. #19153749 | C4 | semidirect |
| 20. #19153749 | C4 | semidirect |
| 21. #19153748 | C4 | semidirect |
| 22. #106×C181 | C4 | semidirect |
| 88. C181 | #1922 | semidirect |
| 107. #106 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042286 | 2 |
| #26042244 | 2 |
| #26042155 | 2 |
| #26042149 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| #26041314 | 2 |
| #1922 | 181 |