Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×#64527 | C2 | semidirect |
| 3. C2×#10597393 | C2 | semidirect |
| 4. #11926929 | C2 | direct (N × H) |
| 5. C2×C8×Dic19 | C2 | semidirect |
| 6. C22×Q16×C19 | C2 | semidirect |
| 10. C2×Q16×C19 | C22 | semidirect |
| 13. #10597393 | C22 | semidirect |
| 15. C2×#64527 | C22 | semidirect |
| 21. C8×Dic19 | C22 | semidirect |
| 76. C22×Q16 | D19 | semidirect |
| 82. C2×C19 | #495 | semidirect |
| 89. C2×Q16 | C2×D19 | semidirect |
| 101. C19 | C2×#495 | semidirect |
| 156. C2 | #11926929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64527 | 2 |
| C22×D152 | 2 |
| C2×#10597393 | 2 |
| #11926929 | 2 |
| C2×C8×Dic19 | 2 |
| C22×Q16×C19 | 2 |
| C2×#495 | 19 |