Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 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. #26041824 | C2 | semidirect |
| 2. C2×#19153805 | C2 | semidirect |
| 3. #26041665 | C2 | semidirect |
| 4. #26041640 | C2 | semidirect |
| 5. #26041497 | C2 | semidirect |
| 6. #26041496 | C2 | semidirect |
| 7. #26041418 | C2 | semidirect |
| 8. #26041415 | C2 | semidirect |
| 9. #26041412 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #448×C181 | C2 | semidirect |
| 14. C2×#15668436 | C22 | semidirect |
| 17. #19153815 | C22 | semidirect |
| 18. #19153812 | C22 | semidirect |
| 26. D4×Dic181 | C22 | semidirect |
| 27. #19153778 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153740 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 39. C2×SD16×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 152. C181 | #3213 | semidirect |
| 161. #448 | D181 | semidirect |
| 169. C2×SD16 | C2×D181 | semidirect |
| 190. #103 | 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×#19153805 | 2 |
| #26041665 | 2 |
| #26041640 | 2 |
| #26041497 | 2 |
| #26041496 | 2 |
| #26041418 | 2 |
| #26041415 | 2 |
| #26041412 | 2 |
| #26041333 | 2 |
| #448×C181 | 2 |
| #3213 | 181 |