Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #11926936 | C2 | semidirect |
| 3. #11926918 | C2 | semidirect |
| 4. #11926910 | C2 | semidirect |
| 5. #11926901 | C2 | semidirect |
| 6. #11926766 | C2 | semidirect |
| 7. #11926744 | C2 | semidirect |
| 8. #11926704 | C2 | semidirect |
| 9. #11926694 | C2 | semidirect |
| 10. #11926605 | C2 | semidirect |
| 11. C19×#541 | C2 | semidirect |
| 14. C19×C4⋊Q8 | C22 | semidirect |
| 17. C19×#125 | C22 | semidirect |
| 19. C4×Q8×C19 | C22 | semidirect |
| 21. C2×#64528 | C22 | semidirect |
| 24. C2×#64527 | C22 | semidirect |
| 32. #10597267 | C22 | semidirect |
| 35. #10597266 | C22 | semidirect |
| 36. C4⋊(C19⋊C8) | C22 | semidirect |
| 37. #10597260 | C22 | semidirect |
| 38. C4×C19⋊C8 | C22 | semidirect |
| 117. #541 | D19 | semidirect |
| 140. C4⋊Q8 | C2×D19 | semidirect |
| 145. #125 | C2×D19 | semidirect |
| 151. C4×Q8 | C2×D19 | semidirect |
| 161. C19 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927113 | 2 |
| #11926936 | 2 |
| #11926918 | 2 |
| #11926910 | 2 |
| #11926901 | 2 |
| #11926766 | 2 |
| #11926744 | 2 |
| #11926704 | 2 |
| #11926694 | 2 |
| #11926605 | 2 |
| C19×#541 | 2 |
| #3222 | 19 |