Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 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. #26041831 | C2 | semidirect |
| 3. #26041609 | C2 | semidirect |
| 4. #26041568 | C2 | semidirect |
| 5. #26041483 | C2 | semidirect |
| 8. #26041366 | C2 | semidirect |
| 9. #26041364 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #483×C181 | C2 | semidirect |
| 16. #19153815 | C22 | semidirect |
| 17. #19153814 | C22 | semidirect |
| 21. Q8×Dic181 | C22 | semidirect |
| 23. #19153781 | C22 | semidirect |
| 31. #19153747 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153739 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 94. C2×Dic181 | SD16 | semidirect |
| 136. C181 | #3101 | semidirect |
| 141. #483 | D181 | semidirect |
| 171. #106 | C2×D181 | semidirect |
| 174. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153778 | 2 |
| #26041609 | 2 |
| #26041568 | 2 |
| #26041483 | 2 |
| #26041432 | 2 |
| #26041429 | 2 |
| #26041366 | 2 |
| #26041364 | 2 |
| #26041329 | 2 |
| #483×C181 | 2 |
| #3101 | 181 |