Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041994 | C2 | semidirect |
| 2. D4×D724 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041606 | C2 | semidirect |
| 5. #26041569 | C2 | semidirect |
| 6. #26041531 | C2 | semidirect |
| 7. #26041474 | C2 | semidirect |
| 8. #26041411 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. C4×D8×C181 | C2 | semidirect |
| 14. C2×#15668434 | C22 | semidirect |
| 15. C2×#15668432 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 22. #19153787 | C22 | semidirect |
| 26. #19153774 | C22 | semidirect |
| 27. #19153747 | C22 | semidirect |
| 28. C4⋊#13089678 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. #19153736 | C22 | semidirect |
| 33. #19153728 | C22 | semidirect |
| 36. C4×D4×C181 | C22 | semidirect |
| 37. #107×C181 | C22 | semidirect |
| 39. #102×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 140. C181 | #3325 | semidirect |
| 150. C4×D8 | D181 | semidirect |
| 168. C4×D4 | C2×D181 | semidirect |
| 171. #107 | C2×D181 | semidirect |
| 179. #102 | C2×D181 | semidirect |
| 181. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| D4×D724 | 2 |
| #26041626 | 2 |
| #26041606 | 2 |
| #26041569 | 2 |
| #26041531 | 2 |
| #26041474 | 2 |
| #26041411 | 2 |
| #26041358 | 2 |
| #26041282 | 2 |
| C4×D8×C181 | 2 |
| #3325 | 181 |