Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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. C24×Dic181 | C2 | semidirect |
| 3. C2×#19153776 | C2 | semidirect |
| 4. #26041156 | C2 | semidirect |
| 5. #26041151 | C2 | semidirect |
| 6. C22⋊C4×Dic181 | C2 | semidirect |
| 7. #379×C181 | C2 | semidirect |
| 12. C22×C4×D181 | C22 | semidirect |
| 13. #19153785 | C4 | semidirect |
| 15. C2×#15668428 | C22 | semidirect |
| 17. C2×#15668426 | C22 | semidirect |
| 18. C2×C4×Dic181 | C22 | semidirect |
| 19. #19153723 | C22 | semidirect |
| 26. C2×C22⋊D181 | C2×C4 | semidirect |
| 31. C22×Dic181 | D4 | semidirect |
| 37. C22⋊Dic181 | C2×C4 | semidirect |
| 42. C24×C181 | C2×C4 | semidirect |
| 50. C22×D181 | C22×C4 | semidirect |
| 57. C2×Dic181 | C22×C4 | semidirect |
| 78. C22×C181 | C4×D4 | semidirect |
| 89. Dic181 | #120 | semidirect |
| 95. C181 | C4×#120 | semidirect |
| 102. #379 | D181 | semidirect |
| 122. C24 | C4×D181 | semidirect |
| 177. C22 | #19153776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic181 | 2 |
| C2×#19153785 | 2 |
| C2×#19153776 | 2 |
| #26041156 | 2 |
| #26041151 | 2 |
| C22⋊C4×Dic181 | 2 |
| #379×C181 | 2 |
| C4×#120 | 181 |