Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#64545 | C2 | semidirect |
| 2. C2×#10597395 | C2 | semidirect |
| 3. #11927051 | C2 | semidirect |
| 4. #11926705 | C2 | semidirect |
| 5. #11926688 | C2 | semidirect |
| 6. #11926553 | C2 | semidirect |
| 7. #11926550 | C2 | semidirect |
| 8. #11926507 | C2 | semidirect |
| 9. C2×C19×#137 | C2 | semidirect |
| 21. C2×Q16×C19 | C22 | semidirect |
| 22. C2×SD16×C19 | C22 | semidirect |
| 25. #10597392 | C22 | semidirect |
| 26. C2×#64527 | C22 | semidirect |
| 27. #10597384 | C22 | semidirect |
| 30. C2×#64525 | C22 | semidirect |
| 34. #10597292 | C22 | semidirect |
| 35. #10597278 | C22 | semidirect |
| 36. (C2×D19)⋊C8 | C22 | semidirect |
| 43. C2×Q8×C19 | D4 | semidirect |
| 60. C2×D76 | D4 | semidirect |
| 141. C2×#137 | D19 | semidirect |
| 167. C2×Q16 | C2×D19 | semidirect |
| 169. C2×SD16 | C2×D19 | semidirect |
| 182. C19 | #3005 | semidirect |
| 192. C2×Q8 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64545 | 2 |
| C2×#10597395 | 2 |
| #11927051 | 2 |
| #11926705 | 2 |
| #11926688 | 2 |
| #11926553 | 2 |
| #11926550 | 2 |
| #11926507 | 2 |
| C2×C19×#137 | 2 |
| #3005 | 19 |