Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041815 | C2 | semidirect |
| 2. C2×#19153805 | C2 | semidirect |
| 3. #26041664 | C2 | semidirect |
| 4. #26041635 | C2 | semidirect |
| 5. #26041503 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041429 | C2 | semidirect |
| 8. #26041418 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #451×C181 | C2 | semidirect |
| 14. C2×#15668436 | C22 | semidirect |
| 17. #19153807 | C22 | semidirect |
| 22. #19153805 | C22 | semidirect |
| 25. Q8×Dic181 | C22 | semidirect |
| 26. #19153778 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 39. C2×Q16×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 143. C181 | #3211 | semidirect |
| 151. #451 | D181 | semidirect |
| 158. C2×Q16 | C2×D181 | semidirect |
| 181. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×#19153805 | 2 |
| #26041664 | 2 |
| #26041635 | 2 |
| #26041503 | 2 |
| #26041497 | 2 |
| #26041429 | 2 |
| #26041418 | 2 |
| #26041415 | 2 |
| #26041329 | 2 |
| #451×C181 | 2 |
| #3211 | 181 |