Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19153843 | C2 | semidirect |
| 2. #26041922 | C2 | semidirect |
| 3. #26041522 | C2 | semidirect |
| 4. #26041491 | C2 | semidirect |
| 5. #26041440 | C2 | semidirect |
| 6. #26041411 | C2 | semidirect |
| 7. C4×D1448 | C2 | semidirect |
| 8. #26041358 | C2 | semidirect |
| 9. #495×C181 | C2 | semidirect |
| 11. C2×D4×D181 | C22 | semidirect |
| 13. C2×#15668436 | C22 | semidirect |
| 16. C2×#15668432 | C22 | semidirect |
| 18. #19153792 | C22 | semidirect |
| 23. C4×D724 | C22 | semidirect |
| 25. #19153750 | C22 | semidirect |
| 26. C4⋊#13089678 | C22 | semidirect |
| 27. #19153740 | C22 | semidirect |
| 28. #19153738 | C22 | semidirect |
| 29. #19153737 | C22 | semidirect |
| 30. #19153728 | C22 | semidirect |
| 31. C2×Q16×C181 | C22 | semidirect |
| 32. C2×SD16×C181 | C22 | semidirect |
| 34. #124×C181 | C22 | semidirect |
| 35. C4×C8×C181 | C22 | semidirect |
| 50. D1448 | D4 | semidirect |
| 124. C181 | #3273 | semidirect |
| 128. #495 | D181 | semidirect |
| 138. C2×Q16 | C2×D181 | semidirect |
| 140. C2×SD16 | C2×D181 | semidirect |
| 145. #124 | C2×D181 | semidirect |
| 160. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153843 | 2 |
| #26041922 | 2 |
| #26041522 | 2 |
| #26041491 | 2 |
| #26041440 | 2 |
| #26041411 | 2 |
| C4×D1448 | 2 |
| #26041358 | 2 |
| #495×C181 | 2 |
| #3273 | 181 |