Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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×D4×Dic181 | C2 | semidirect |
| 3. #26041593 | C2 | semidirect |
| 4. #26041590 | C2 | semidirect |
| 5. #26041557 | C2 | semidirect |
| 6. #26041472 | C2 | semidirect |
| 7. #26041413 | C2 | semidirect |
| 8. D8×Dic181 | C2 | semidirect |
| 9. #26041359 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #447×C181 | C2 | semidirect |
| 15. #19153815 | C22 | semidirect |
| 16. #19153812 | C22 | semidirect |
| 24. D4×Dic181 | C22 | semidirect |
| 25. #19153778 | C22 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 96. C2×Dic181 | D8 | semidirect |
| 113. D4×C181 | #41 | semidirect |
| 149. C181 | #3100 | semidirect |
| 158. #447 | D181 | semidirect |
| 249. D4 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×D4×Dic181 | 2 |
| #26041593 | 2 |
| #26041590 | 2 |
| #26041557 | 2 |
| #26041472 | 2 |
| #26041413 | 2 |
| D8×Dic181 | 2 |
| #26041359 | 2 |
| #26041329 | 2 |
| #447×C181 | 2 |
| #3100 | 181 |