Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597360 | C2 | semidirect |
| 2. #11927216 | C2 | semidirect |
| 3. #11927179 | C2 | semidirect |
| 4. #11926920 | C2 | semidirect |
| 5. #11926796 | C2 | semidirect |
| 6. #11926740 | C2 | semidirect |
| 7. #11926688 | C2 | semidirect |
| 8. #11926679 | C2 | semidirect |
| 9. C4×#64527 | C2 | semidirect |
| 10. #11926621 | C2 | semidirect |
| 11. C19×#460 | C2 | semidirect |
| 12. C2×#64545 | C22 | semidirect |
| 15. C2×SD16×C19 | C22 | semidirect |
| 17. C4×Q8×C19 | C22 | semidirect |
| 22. C2×#64525 | C22 | semidirect |
| 23. C2×#64525 | C22 | semidirect |
| 26. C2×#64515 | C22 | semidirect |
| 28. #10597341 | C22 | semidirect |
| 30. #10597320 | C22 | semidirect |
| 34. C19×C4⋊C8 | C22 | semidirect |
| 35. C19×#102 | C22 | semidirect |
| 36. #10597292 | C22 | semidirect |
| 37. #10597278 | C22 | semidirect |
| 38. (C2×D19)⋊C8 | C22 | semidirect |
| 40. #10597265 | C22 | semidirect |
| 41. C4×C19⋊C8 | C22 | semidirect |
| 71. #64527 | D4 | semidirect |
| 91. Q8×C19 | C2×D4 | semidirect |
| 120. C19⋊C8 | C2×D4 | semidirect |
| 139. C4×C19 | AGL(1,ℤ/8) | semidirect |
| 149. #460 | D19 | semidirect |
| 167. C2×SD16 | C2×D19 | semidirect |
| 180. C4×Q8 | C2×D19 | semidirect |
| 185. C4⋊C8 | C2×D19 | semidirect |
| 189. #102 | C2×D19 | semidirect |
| 192. C19 | #3274 | semidirect |
| 242. Q8 | D4×D19 | semidirect |
| 291. C4 | #10597360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597360 | 2 |
| #11927216 | 2 |
| #11927179 | 2 |
| #11926920 | 2 |
| #11926796 | 2 |
| #11926740 | 2 |
| #11926688 | 2 |
| #11926679 | 2 |
| C4×#64527 | 2 |
| #11926621 | 2 |
| C19×#460 | 2 |
| #3274 | 19 |