Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041831 | C2 | semidirect |
| 3. #26041650 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041478 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041432 | C2 | semidirect |
| 8. #26041430 | C2 | semidirect |
| 9. #26041429 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #450×C181 | C2 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 16. C2×#15668437 | C22 | semidirect |
| 17. C2×#15668436 | C22 | semidirect |
| 18. #19153815 | C22 | semidirect |
| 19. #19153814 | C22 | semidirect |
| 27. Q8×Dic181 | C22 | semidirect |
| 29. #19153781 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 39. C2×SD16×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 102. C2×Dic181 | SD16 | semidirect |
| 151. C181 | #3208 | semidirect |
| 162. #450 | D181 | semidirect |
| 171. C2×SD16 | C2×D181 | semidirect |
| 191. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153812 | 2 |
| #26041650 | 2 |
| #26041624 | 2 |
| #26041478 | 2 |
| #26041477 | 2 |
| #26041432 | 2 |
| #26041430 | 2 |
| #26041429 | 2 |
| #26041329 | 2 |
| #450×C181 | 2 |
| #3208 | 181 |