Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041815 | C2 | semidirect |
| 2. C2×#19153778 | C2 | semidirect |
| 3. #26041592 | C2 | semidirect |
| 4. #26041578 | C2 | semidirect |
| 5. #26041497 | C2 | semidirect |
| 6. #26041429 | C2 | semidirect |
| 8. #26041390 | C2 | semidirect |
| 9. #26041382 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #483×C181 | C2 | semidirect |
| 17. #19153807 | C22 | semidirect |
| 18. #19153805 | C22 | semidirect |
| 21. Q8×Dic181 | C22 | semidirect |
| 26. #19153778 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 140. C181 | #3114 | semidirect |
| 144. #483 | D181 | semidirect |
| 175. #106 | C2×D181 | semidirect |
| 177. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×#19153778 | 2 |
| #26041592 | 2 |
| #26041578 | 2 |
| #26041497 | 2 |
| #26041429 | 2 |
| #26041415 | 2 |
| #26041390 | 2 |
| #26041382 | 2 |
| #26041333 | 2 |
| #483×C181 | 2 |
| #3114 | 181 |