Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 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×#10597378 | C2 | semidirect |
| 2. #11927199 | C2 | semidirect |
| 3. #11926916 | C2 | semidirect |
| 4. #11926788 | C2 | semidirect |
| 5. #11926749 | C2 | semidirect |
| 6. #11926736 | C2 | semidirect |
| 7. #11926695 | C2 | semidirect |
| 8. #11926687 | C2 | semidirect |
| 9. C4×#64525 | C2 | semidirect |
| 10. #11926622 | C2 | semidirect |
| 11. D42×C19 | C2 | semidirect |
| 14. C2×#64541 | C22 | semidirect |
| 23. C2×#64526 | C22 | semidirect |
| 24. C2×#64526 | C22 | semidirect |
| 27. C2×#64525 | C22 | semidirect |
| 28. #10597370 | C22 | semidirect |
| 29. C2×#64520 | C22 | semidirect |
| 32. C4×D76 | C22 | semidirect |
| 33. #10597315 | C22 | semidirect |
| 35. #10597289 | C22 | semidirect |
| 36. C22⋊(C19⋊C8) | C22 | semidirect |
| 37. #10597267 | C22 | semidirect |
| 38. #10597266 | C22 | semidirect |
| 39. #10597264 | C22 | semidirect |
| 40. C4⋊(C19⋊C8) | C22 | semidirect |
| 41. C4×C19⋊C8 | C22 | semidirect |
| 73. #64525 | D4 | semidirect |
| 111. D76 | C2×D4 | semidirect |
| 118. C19⋊C8 | C2×D4 | semidirect |
| 137. C4×C19 | AGL(1,ℤ/8) | semidirect |
| 144. D42 | D19 | semidirect |
| 190. C19 | #3272 | semidirect |
| 287. C4 | #10597378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597378 | 2 |
| #11927199 | 2 |
| #11926916 | 2 |
| #11926788 | 2 |
| #11926749 | 2 |
| #11926736 | 2 |
| #11926695 | 2 |
| #11926687 | 2 |
| C4×#64525 | 2 |
| #11926622 | 2 |
| D42×C19 | 2 |
| #3272 | 19 |