Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 400 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. #26041834 | C2 | semidirect |
| 3. #26041671 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041638 | C2 | semidirect |
| 6. #26041503 | C2 | semidirect |
| 7. #26041499 | C2 | semidirect |
| 8. #26041433 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #497×C181 | C2 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 25. Q8×Dic181 | C22 | semidirect |
| 31. #19153745 | C22 | semidirect |
| 32. #19153741 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 37. #19153727 | C22 | semidirect |
| 38. C2×Q16×C181 | C22 | semidirect |
| 40. C4⋊Q8×C181 | C22 | semidirect |
| 42. #97×C181 | C22 | semidirect |
| 142. C181 | #3215 | semidirect |
| 147. #497 | D181 | semidirect |
| 158. C2×Q16 | C2×D181 | semidirect |
| 162. C4⋊Q8 | C2×D181 | semidirect |
| 185. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #124×D181 | 2 |
| #26041671 | 2 |
| #26041639 | 2 |
| #26041638 | 2 |
| #26041503 | 2 |
| #26041499 | 2 |
| #26041433 | 2 |
| #26041428 | 2 |
| #26041334 | 2 |
| #497×C181 | 2 |
| #3215 | 181 |