Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#19153823 | C2 | semidirect |
| 2. #26041762 | C2 | semidirect |
| 3. #26041284 | C2 | semidirect |
| 4. #26041280 | C2 | semidirect |
| 5. #26041275 | C2 | semidirect |
| 6. C2×#19153737 | C2 | semidirect |
| 9. C2×#15668433 | C22 | semidirect |
| 10. C22×#13089678 | C22 | semidirect |
| 13. #19153775 | C22 | semidirect |
| 14. C2×C4⋊Dic181 | C22 | semidirect |
| 15. #19153740 | C22 | semidirect |
| 16. #19153740 | C22 | semidirect |
| 17. #19153737 | C22 | semidirect |
| 18. #19153737 | C22 | semidirect |
| 19. #19153737 | C22 | semidirect |
| 21. H(5,𝔽2)×C181 | C4 | semidirect |
| 41. #41×C181 | C2×C4 | semidirect |
| 49. C2×D4×C181 | C2×C4 | semidirect |
| 97. C181 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic181 | semidirect |
| 129. #41 | C2×Dic181 | semidirect |
| 137. C2×D4 | C2×Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| #26041762 | 2 |
| #26041284 | 2 |
| #26041280 | 2 |
| #26041275 | 2 |
| C2×#19153737 | 2 |
| C2×H(5,𝔽2)×C181 | 2 |
| #2897 | 181 |