Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041885 | C2 | semidirect |
| 2. #26041842 | C2 | semidirect |
| 3. #26041668 | C2 | semidirect |
| 4. #26041655 | C2 | semidirect |
| 5. #26041636 | C2 | semidirect |
| 6. #26041493 | C2 | semidirect |
| 7. #26041473 | C2 | semidirect |
| 8. #26041425 | C2 | semidirect |
| 9. #26041414 | C2 | semidirect |
| 10. #26041341 | C2 | semidirect |
| 11. #490×C181 | C2 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 17. C2×#15668434 | C22 | semidirect |
| 18. #19153813 | C22 | semidirect |
| 27. #19153778 | C22 | semidirect |
| 29. #19153745 | C22 | semidirect |
| 30. #19153739 | C22 | semidirect |
| 33. C4×#13089678 | C22 | semidirect |
| 35. #125×C181 | C22 | semidirect |
| 37. #102×C181 | C22 | semidirect |
| 38. #97×C181 | C22 | semidirect |
| 128. C181 | #3220 | semidirect |
| 134. #490 | D181 | semidirect |
| 150. #125 | C2×D181 | semidirect |
| 164. #102 | C2×D181 | semidirect |
| 166. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041885 | 2 |
| #26041842 | 2 |
| #26041668 | 2 |
| #26041655 | 2 |
| #26041636 | 2 |
| #26041493 | 2 |
| #26041473 | 2 |
| #26041425 | 2 |
| #26041414 | 2 |
| #26041341 | 2 |
| #490×C181 | 2 |
| #3220 | 181 |