Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10597255 | C2 | semidirect |
| 3. M32×D19 | C2 | semidirect |
| 4. #11926329 | C2 | semidirect |
| 5. #11926328 | C2 | semidirect |
| 6. #11926327 | C2 | semidirect |
| 7. C19×#350 | C2 | semidirect |
| 19. C19×M32 | C22 | semidirect |
| 20. C2×C16×C19 | C22 | semidirect |
| 21. #10597269 | C22 | semidirect |
| 22. C2×C19⋊C16 | C22 | semidirect |
| 109. #350 | D19 | semidirect |
| 131. M32 | C2×D19 | semidirect |
| 134. C2×C16 | C2×D19 | semidirect |
| 135. C19 | #2117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D19 | 2 |
| C2×#10597255 | 2 |
| M32×D19 | 2 |
| #11926329 | 2 |
| #11926328 | 2 |
| #11926327 | 2 |
| C19×#350 | 2 |
| #2117 | 19 |