Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19153813 | C2 | semidirect |
| 2. #26041813 | C2 | semidirect |
| 3. #26041668 | C2 | semidirect |
| 4. #26041644 | C2 | semidirect |
| 5. #26041480 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041432 | C2 | semidirect |
| 8. #26041415 | C2 | semidirect |
| 9. #432×C181 | C2 | semidirect |
| 13. C2×#15668438 | C22 | semidirect |
| 14. C2×D1448 | C22 | semidirect |
| 20. #19153808 | C22 | semidirect |
| 21. #19153804 | C22 | semidirect |
| 25. C4×Dic362 | C22 | semidirect |
| 26. C4×D724 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. C4⋊C8×C181 | C22 | semidirect |
| 34. #97×C181 | C22 | semidirect |
| 127. C181 | #3217 | semidirect |
| 137. #432 | D181 | semidirect |
| 158. C4⋊C8 | C2×D181 | semidirect |
| 162. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| #26041813 | 2 |
| #26041668 | 2 |
| #26041644 | 2 |
| #26041480 | 2 |
| #26041475 | 2 |
| #26041432 | 2 |
| #26041415 | 2 |
| #432×C181 | 2 |
| #3217 | 181 |