Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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 |
|---|---|---|
| 1. C2×#19153903 | C2 | direct (N × H) |
| 2. C22×#15668459 | C2 | semidirect |
| 3. C22×#15668458 | C2 | semidirect |
| 4. C22×D181⋊C8 | C2 | semidirect |
| 5. C23×#13089685 | C2 | semidirect |
| 7. #19153903 | C22 | direct (N × H) |
| 8. C2×#15668459 | C22 | semidirect |
| 9. C2×#15668458 | C22 | semidirect |
| 10. C2×D181⋊C8 | C22 | semidirect |
| 14. C22×#13089685 | C22 | semidirect |
| 22. #15668459 | C23 | semidirect |
| 23. #15668458 | C23 | semidirect |
| 24. D181⋊C8 | C23 | semidirect |
| 28. C2×#13089685 | C23 | semidirect |
| 63. C22×C181 | #131 | semidirect |
| 73. C2×C181 | C2×#131 | semidirect |
| 76. C181 | C22×#131 | semidirect |
| 142. C22 | #19153903 | direct (N × H) |
| 151. C2 | C2×#19153903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153903 | 2 |
| C22×#15668459 | 2 |
| C22×#15668458 | 2 |
| C22×D181⋊C8 | 2 |
| C23×#13089685 | 2 |
| C22×#15668448 | 2 |
| C22×#131 | 181 |