Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 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. #26041824 | C2 | semidirect |
| 2. C2×#19153812 | C2 | semidirect |
| 3. #26041654 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041473 | C2 | semidirect |
| 6. #26041472 | C2 | semidirect |
| 7. #26041415 | C2 | semidirect |
| 8. #26041413 | C2 | semidirect |
| 9. #26041412 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #447×C181 | C2 | semidirect |
| 16. C2×D1448 | C22 | semidirect |
| 17. C2×#15668434 | C22 | semidirect |
| 18. C2×#15668434 | C22 | semidirect |
| 19. #19153815 | C22 | semidirect |
| 24. #19153812 | C22 | semidirect |
| 28. D4×Dic181 | C22 | semidirect |
| 29. #19153778 | 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×D8×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 107. C2×Dic181 | D8 | semidirect |
| 164. C181 | #3205 | semidirect |
| 175. #447 | D181 | semidirect |
| 185. C2×D8 | C2×D181 | semidirect |
| 204. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×#19153812 | 2 |
| #26041654 | 2 |
| #26041624 | 2 |
| #26041473 | 2 |
| #26041472 | 2 |
| #26041415 | 2 |
| #26041413 | 2 |
| #26041412 | 2 |
| #26041329 | 2 |
| #447×C181 | 2 |
| #3205 | 181 |