Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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 | semidirect |
| 4. #26042169 | C2 | semidirect |
| 9. #19153890 | C4 | semidirect |
| 10. D181⋊C16 | C4 | semidirect |
| 16. #19153756 | C4 | semidirect |
| 18. C16×D181 | C4 | semidirect |
| 19. M32×C181 | C4 | semidirect |
| 28. #15668452 | C2×C4 | semidirect |
| 35. #15668424 | C2×C4 | semidirect |
| 37. C16×C181 | C2×C4 | semidirect |
| 67. D181 | #347 | semidirect |
| 68. C181 | C2×#347 | semidirect |
| 82. M32 | #10624382 | semidirect |
| 106. C16 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊M32 | 2 |
| C2×#19153870 | 2 |
| #26042170 | 2 |
| #26042169 | 2 |
| M32×D181 | 2 |
| C2×#347 | 181 |