Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D181 | C2 | semidirect |
| 2. C2×#19153845 | C2 | semidirect |
| 4. #26041437 | C2 | semidirect |
| 5. #26041436 | C2 | semidirect |
| 6. #26041435 | C2 | semidirect |
| 7. #26041417 | C2 | semidirect |
| 8. #26041416 | C2 | semidirect |
| 9. #26041286 | C2 | semidirect |
| 10. #26041241 | C2 | semidirect |
| 11. #448×C181 | C2 | semidirect |
| 23. C2×Dic724 | C22 | semidirect |
| 24. C2×#15668439 | C22 | semidirect |
| 25. C2×#15668437 | C22 | semidirect |
| 35. #19153741 | C22 | semidirect |
| 36. #19153740 | C22 | semidirect |
| 37. #19153739 | C22 | semidirect |
| 41. C2×SD16×C181 | C22 | semidirect |
| 43. #103×C181 | C22 | semidirect |
| 59. Q8×D181 | D4 | semidirect |
| 144. C22×C181 | #137 | semidirect |
| 152. C2×D181 | #137 | semidirect |
| 169. C181 | #3004 | semidirect |
| 179. #448 | D181 | semidirect |
| 197. C2×SD16 | C2×D181 | semidirect |
| 211. #103 | C2×D181 | semidirect |
| 321. C22 | #19153845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D181 | 2 |
| C2×#19153845 | 2 |
| #26041789 | 2 |
| #26041437 | 2 |
| #26041436 | 2 |
| #26041435 | 2 |
| #26041417 | 2 |
| #26041416 | 2 |
| #26041286 | 2 |
| #26041241 | 2 |
| #448×C181 | 2 |
| #3004 | 181 |