Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C2×#10597388 | C2 | semidirect |
| 2. C2×#10597378 | C2 | semidirect |
| 3. C2×#10597350 | C2 | semidirect |
| 4. #11927118 | C2 | semidirect |
| 5. #11927111 | C2 | semidirect |
| 6. #11926935 | C2 | semidirect |
| 7. #11926930 | C2 | semidirect |
| 8. #11926925 | C2 | semidirect |
| 9. #11926915 | C2 | semidirect |
| 10. #11926499 | C2 | semidirect |
| 11. C22×SD16×C19 | C2 | semidirect |
| 21. #10597393 | C22 | semidirect |
| 23. #10597390 | C22 | semidirect |
| 24. C2×#64528 | C22 | semidirect |
| 26. C2×#64527 | C22 | semidirect |
| 36. C2×Dic76 | C22 | semidirect |
| 38. C2×D152 | C22 | semidirect |
| 39. C2×#64516 | C22 | semidirect |
| 40. C2×#64516 | C22 | semidirect |
| 41. #10597272 | C22 | semidirect |
| 42. C8×Dic19 | C22 | semidirect |
| 69. C2×C8×C19 | D4 | semidirect |
| 82. #64520 | D4 | semidirect |
| 146. C22×SD16 | D19 | semidirect |
| 191. C19 | #3154 | semidirect |
| 228. C2×C8 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597388 | 2 |
| C2×#10597378 | 2 |
| C2×#10597350 | 2 |
| #11927118 | 2 |
| #11927111 | 2 |
| #11926935 | 2 |
| #11926930 | 2 |
| #11926925 | 2 |
| #11926915 | 2 |
| #11926499 | 2 |
| C22×SD16×C19 | 2 |
| #3154 | 19 |