Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 146 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. #26042149 | C2 | direct (N × H) |
| 8. C2×#15668459 | C4 | semidirect |
| 13. C2×C4×#10624382 | C4 | semidirect |
| 18. #19153774 | C4 | semidirect |
| 20. C2×C4⋊Dic181 | C4 | semidirect |
| 23. C2×C4⋊C4×C181 | C4 | semidirect |
| 30. #15668459 | C2×C4 | semidirect |
| 35. C4×#10624382 | C2×C4 | semidirect |
| 48. C4⋊Dic181 | C2×C4 | semidirect |
| 56. C4⋊C4×C181 | C2×C4 | semidirect |
| 113. C2×C181 | #339 | semidirect |
| 120. C181 | C2×#339 | semidirect |
| 138. C2×C4⋊C4 | #10624382 | semidirect |
| 170. C4⋊C4 | C2×#10624382 | semidirect |
| 237. C2 | #26042149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C22×C4×#10624382 | 2 |
| #26042149 | 2 |
| C2×#19153774 | 2 |
| C2×#339 | 181 |