Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 282 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. #26042243 | C2 | semidirect |
| 3. C4×#15668458 | C2 | semidirect |
| 5. C2×#15668458 | C4 | semidirect |
| 9. #19153871 | C22 | semidirect |
| 10. C4×#13089685 | C22 | semidirect |
| 19. #15668458 | C2×C4 | semidirect |
| 20. C2×#13089685 | C2×C4 | semidirect |
| 67. C181 | #2873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668458 | 2 |
| #26042243 | 2 |
| C4×#15668458 | 2 |
| C2×#19153772 | 2 |
| #2873 | 181 |