Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
168 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #26042170 | C2 | direct (N × H) |
| 7. #19153891 | C4 | semidirect |
| 9. C2×#15668452 | C4 | semidirect |
| 13. #19153755 | C4 | semidirect |
| 15. C2×#15668424 | C4 | semidirect |
| 16. C2×C16×C181 | C4 | semidirect |
| 23. #15668452 | C2×C4 | semidirect |
| 30. #15668424 | C2×C4 | semidirect |
| 32. C16×C181 | C2×C4 | semidirect |
| 56. C2×C181 | #347 | semidirect |
| 60. C181 | C2×#347 | semidirect |
| 75. C2×C16 | #10624382 | semidirect |
| 93. C16 | C2×#10624382 | semidirect |
| 119. C2 | #26042170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153891 | 2 |
| C2×#19153870 | 2 |
| #26042170 | 2 |
| C2×#19153755 | 2 |
| C2×#347 | 181 |