Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×#19153876 | C2 | semidirect |
| 2. C2×#19153874 | C2 | semidirect |
| 3. #26042179 | C2 | direct (N × H) |
| 8. #19153876 | C22 | semidirect |
| 10. #19153874 | C22 | semidirect |
| 15. #19153785 | C4 | semidirect |
| 18. C2×C22⋊Dic181 | C4 | semidirect |
| 19. C25×C181 | C4 | semidirect |
| 41. C22⋊Dic181 | C2×C4 | semidirect |
| 48. C24×C181 | C2×C4 | semidirect |
| 120. C2×C181 | AΣL(1,𝔽16) | semidirect |
| 124. C181 | C2×AΣL(1,𝔽16) | semidirect |
| 130. C25 | #10624382 | semidirect |
| 152. C24 | C2×#10624382 | semidirect |
| 247. C2 | #26042179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153876 | 2 |
| C2×#19153874 | 2 |
| #26042179 | 2 |
| C2×#19153785 | 2 |
| C2×AΣL(1,𝔽16) | 181 |