Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041827 | C2 | semidirect |
| 2. #124×D181 | C2 | semidirect |
| 3. #26041666 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041638 | C2 | semidirect |
| 6. #26041496 | C2 | semidirect |
| 7. #26041492 | C2 | semidirect |
| 8. #26041416 | C2 | semidirect |
| 9. #26041411 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #496×C181 | C2 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 17. #19153816 | C22 | semidirect |
| 27. D4×Dic181 | C22 | semidirect |
| 31. #19153745 | C22 | semidirect |
| 32. #19153741 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 37. #19153727 | C22 | semidirect |
| 38. C2×SD16×C181 | C22 | semidirect |
| 40. #127×C181 | C22 | semidirect |
| 42. #97×C181 | C22 | semidirect |
| 150. C181 | #3213 | semidirect |
| 155. #496 | D181 | semidirect |
| 167. C2×SD16 | C2×D181 | semidirect |
| 171. #127 | C2×D181 | semidirect |
| 193. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| #124×D181 | 2 |
| #26041666 | 2 |
| #26041639 | 2 |
| #26041638 | 2 |
| #26041496 | 2 |
| #26041492 | 2 |
| #26041416 | 2 |
| #26041411 | 2 |
| #26041334 | 2 |
| #496×C181 | 2 |
| #3213 | 181 |