Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 9. #19153886 | C4 | semidirect |
| 11. #19153870 | C4 | semidirect |
| 15. #19153750 | C4 | semidirect |
| 16. #19153747 | C4 | semidirect |
| 17. #107×C181 | C4 | semidirect |
| 69. C181 | #1773 | semidirect |
| 83. #107 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153886 | 2 |
| #26042244 | 2 |
| C2×#19153870 | 2 |
| #26042149 | 2 |
| #26041316 | 2 |
| #1773 | 181 |