Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10597276 | C2 | semidirect |
| 3. #11926352 | C2 | direct (N × H) |
| 4. C22×C16×C19 | C2 | semidirect |
| 17. C2×C16×C19 | C22 | semidirect |
| 19. #10597276 | C22 | semidirect |
| 80. C22×C16 | D19 | semidirect |
| 85. C2×C19 | #359 | semidirect |
| 100. C2×C16 | C2×D19 | semidirect |
| 103. C19 | C2×#359 | semidirect |
| 165. C2 | #11926352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597350 | 2 |
| C2×#10597276 | 2 |
| #11926352 | 2 |
| C22×C16×C19 | 2 |
| C2×#359 | 19 |