Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15668450 | C2 | semidirect |
| 2. C2×#19153839 | C2 | semidirect |
| 3. #26041792 | C2 | semidirect |
| 4. #26041440 | C2 | semidirect |
| 5. #26041429 | C2 | semidirect |
| 6. #26041427 | C2 | semidirect |
| 7. #26041418 | C2 | semidirect |
| 8. #26041415 | C2 | semidirect |
| 9. #26041274 | C2 | semidirect |
| 10. C22⋊C8×D181 | C2 | semidirect |
| 11. #451×C181 | C2 | semidirect |
| 17. C2×#15668450 | C22 | semidirect |
| 23. C2×#15668436 | C22 | semidirect |
| 24. C2×#15668436 | C22 | semidirect |
| 25. C2×D1448 | C22 | semidirect |
| 26. C2×C8×D181 | C22 | semidirect |
| 28. #19153792 | C22 | semidirect |
| 29. #19153791 | C22 | semidirect |
| 34. #19153774 | C22 | semidirect |
| 35. #19153740 | C22 | semidirect |
| 36. #19153738 | C22 | semidirect |
| 37. #19153736 | C22 | semidirect |
| 39. #19153728 | C22 | semidirect |
| 41. C2×Q16×C181 | C22 | semidirect |
| 43. #103×C181 | C22 | semidirect |
| 53. #15668450 | D4 | semidirect |
| 143. C22×C181 | #135 | semidirect |
| 175. C181 | #3002 | semidirect |
| 181. #451 | D181 | semidirect |
| 200. C2×Q16 | C2×D181 | semidirect |
| 215. #103 | C2×D181 | semidirect |
| 333. C22 | #19153839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668450 | 2 |
| C2×#19153839 | 2 |
| #26041792 | 2 |
| #26041440 | 2 |
| #26041429 | 2 |
| #26041427 | 2 |
| #26041418 | 2 |
| #26041415 | 2 |
| #26041274 | 2 |
| C22⋊C8×D181 | 2 |
| #451×C181 | 2 |
| #3002 | 181 |