Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
438 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 54 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. D181⋊#100 | C2 | semidirect |
| 2. D181⋊#99 | C2 | semidirect |
| 3. #26042180 | C2 | semidirect |
| 4. #26042179 | C2 | semidirect |
| 9. #19153876 | C22 | semidirect |
| 11. #19153874 | C22 | semidirect |
| 12. C24×D181 | C4 | semidirect |
| 19. #19153784 | C4 | semidirect |
| 21. C22⋊C4×D181 | C4 | semidirect |
| 22. #120×C181 | C4 | semidirect |
| 35. C23×D181 | C2×C4 | semidirect |
| 49. C22⋊Dic181 | C2×C4 | semidirect |
| 53. C24×C181 | C2×C4 | semidirect |
| 57. C22⋊C4×C181 | C2×C4 | semidirect |
| 147. D181 | AΣL(1,𝔽16) | semidirect |
| 148. C181 | C2×AΣL(1,𝔽16) | semidirect |
| 164. #120 | #10624382 | semidirect |
| 180. C24 | C2×#10624382 | semidirect |
| 206. C22⋊C4 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#100 | 2 |
| D181⋊#99 | 2 |
| #26042180 | 2 |
| #26042179 | 2 |
| #120×D181 | 2 |
| C2×AΣL(1,𝔽16) | 181 |