Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #26042087 | C2 | semidirect |
| 2. #26042081 | C2 | semidirect |
| 3. #26041664 | C2 | semidirect |
| 4. #26041551 | C2 | semidirect |
| 5. #26041549 | C2 | semidirect |
| 6. #26041544 | C2 | semidirect |
| 7. #26041455 | C2 | semidirect |
| 8. #26041452 | C2 | semidirect |
| 9. #26041396 | C2 | semidirect |
| 10. #26041394 | C2 | semidirect |
| 11. #578×C181 | C2 | semidirect |
| 18. #19153841 | C22 | semidirect |
| 23. C2×#15668436 | C22 | semidirect |
| 26. #19153823 | C22 | semidirect |
| 28. #19153805 | C22 | semidirect |
| 29. #19153752 | C22 | semidirect |
| 30. #19153751 | C22 | semidirect |
| 31. #19153743 | C22 | semidirect |
| 32. #19153743 | C22 | semidirect |
| 34. #19153735 | C22 | semidirect |
| 35. #19153732 | C22 | semidirect |
| 36. C8×Dic181 | C22 | semidirect |
| 37. 2−1+4×C181 | C22 | semidirect |
| 39. #137×C181 | C22 | semidirect |
| 43. C2×Q16×C181 | C22 | semidirect |
| 44. #131×C181 | C22 | semidirect |
| 149. C181 | #3290 | semidirect |
| 151. #578 | D181 | semidirect |
| 162. 2−1+4 | C2×D181 | semidirect |
| 167. #137 | C2×D181 | semidirect |
| 178. C2×Q16 | C2×D181 | semidirect |
| 185. #131 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042087 | 2 |
| #26042081 | 2 |
| #26041664 | 2 |
| #26041551 | 2 |
| #26041549 | 2 |
| #26041544 | 2 |
| #26041455 | 2 |
| #26041452 | 2 |
| #26041396 | 2 |
| #26041394 | 2 |
| #578×C181 | 2 |
| #3290 | 181 |