Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C2×#10597388 | C2 | direct (N × H) |
| 3. C22×#64528 | C2 | semidirect |
| 4. C22×#64527 | C2 | semidirect |
| 5. C22×#64520 | C2 | semidirect |
| 6. C23×Q8×C19 | C2 | semidirect |
| 10. C22×Q8×C19 | C22 | semidirect |
| 19. C2×#64528 | C22 | semidirect |
| 20. #10597388 | C22 | direct (N × H) |
| 21. C2×#64527 | C22 | semidirect |
| 22. C2×#64520 | C22 | semidirect |
| 30. C2×Q8×C19 | C23 | semidirect |
| 46. #64528 | C23 | semidirect |
| 47. #64527 | C23 | semidirect |
| 48. #64520 | C23 | semidirect |
| 75. C22×C19 | #137 | semidirect |
| 86. C23×Q8 | D19 | semidirect |
| 92. C2×C19 | C2×#137 | semidirect |
| 101. C22×Q8 | C2×D19 | semidirect |
| 112. C19 | C22×#137 | semidirect |
| 123. C2×Q8 | C22×D19 | semidirect |
| 165. C22 | #10597388 | direct (N × H) |
| 175. C2 | C2×#10597388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64541 | 2 |
| C2×#10597388 | 2 |
| C22×#64528 | 2 |
| C22×#64527 | 2 |
| C22×#64520 | 2 |
| C23×Q8×C19 | 2 |
| C22×#137 | 19 |