Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 1. C22×#15668458 | C2 | semidirect |
| 2. #26042266 | C2 | direct (N × H) |
| 3. C2×#19153877 | C2 | semidirect |
| 4. C2×#19153876 | C2 | semidirect |
| 9. C2×#15668458 | C22 | semidirect |
| 11. #19153877 | C22 | semidirect |
| 12. #19153876 | C22 | semidirect |
| 136. C2×C181 | #413 | semidirect |
| 139. C181 | C2×#413 | semidirect |
| 277. C2 | #26042266 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668458 | 2 |
| #26042266 | 2 |
| C2×#19153877 | 2 |
| C2×#19153876 | 2 |
| C22×#15668448 | 2 |
| C2×#413 | 181 |