Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 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. #26042096 | C2 | semidirect |
| 2. #26042089 | C2 | semidirect |
| 3. #26042080 | C2 | semidirect |
| 4. #26041662 | C2 | semidirect |
| 5. #26041555 | C2 | semidirect |
| 6. #26041541 | C2 | semidirect |
| 7. #26041459 | C2 | semidirect |
| 8. #26041450 | C2 | semidirect |
| 9. #26041395 | C2 | semidirect |
| 10. #26041394 | C2 | semidirect |
| 11. #472×C181 | C2 | semidirect |
| 12. #19153863 | C22 | semidirect |
| 16. #19153849 | C22 | semidirect |
| 27. C2×Dic724 | C22 | semidirect |
| 28. C2×#15668437 | C22 | semidirect |
| 31. #19153824 | C22 | semidirect |
| 33. #19153803 | C22 | semidirect |
| 34. #19153751 | C22 | semidirect |
| 35. #19153743 | C22 | semidirect |
| 37. #19153742 | C22 | semidirect |
| 38. #19153734 | C22 | semidirect |
| 39. C8×Dic181 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C181 | C22 | semidirect |
| 42. #131×C181 | C22 | semidirect |
| 43. #108×C181 | C22 | semidirect |
| 44. #100×C181 | C22 | semidirect |
| 149. C181 | #3290 | semidirect |
| 156. #472 | D181 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D181 | semidirect |
| 185. #131 | C2×D181 | semidirect |
| 188. #108 | C2×D181 | semidirect |
| 193. #100 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042096 | 2 |
| #26042089 | 2 |
| #26042080 | 2 |
| #26041662 | 2 |
| #26041555 | 2 |
| #26041541 | 2 |
| #26041459 | 2 |
| #26041450 | 2 |
| #26041395 | 2 |
| #26041394 | 2 |
| #472×C181 | 2 |
| #3290 | 181 |