Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19153844 | C2 | semidirect |
| 2. C2×#19153836 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041760 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041478 | C2 | semidirect |
| 8. #26041473 | C2 | semidirect |
| 9. #26041307 | C2 | semidirect |
| 10. C2×#19153736 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 16. C2×#15668439 | C22 | semidirect |
| 18. C2×#15668437 | C22 | semidirect |
| 19. C2×#15668436 | C22 | semidirect |
| 21. C2×#15668434 | C22 | semidirect |
| 28. #19153781 | C22 | semidirect |
| 29. #19153778 | C22 | semidirect |
| 34. #19153745 | C22 | semidirect |
| 35. #19153745 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 45. #15668449 | D4 | semidirect |
| 154. C181 | #3045 | semidirect |
| 165. #417 | D181 | semidirect |
| 194. #103 | C2×D181 | semidirect |
| 197. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153836 | 2 |
| #26041843 | 2 |
| #26041760 | 2 |
| #26041504 | 2 |
| #26041497 | 2 |
| #26041478 | 2 |
| #26041473 | 2 |
| #26041307 | 2 |
| C2×#19153736 | 2 |
| #417×C181 | 2 |
| #3045 | 181 |