Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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×#10597372 | C2 | semidirect |
| 3. #11926541 | C2 | direct (N × H) |
| 4. C2×#10597273 | C2 | semidirect |
| 5. C2×#10597278 | C2 | semidirect |
| 6. C23×C8×C19 | C2 | semidirect |
| 11. C2×#64541 | C4 | semidirect |
| 18. C22×C8×C19 | C22 | semidirect |
| 21. #10597372 | C22 | semidirect |
| 24. #10597278 | C22 | semidirect |
| 25. #10597273 | C22 | semidirect |
| 40. #64541 | C2×C4 | semidirect |
| 104. C23×C8 | D19 | semidirect |
| 110. C2×C19 | #416 | semidirect |
| 125. C22×C8 | C2×D19 | semidirect |
| 133. C19 | C2×#416 | semidirect |
| 212. C2 | #11926541 | 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×#10597372 | 2 |
| #11926541 | 2 |
| C2×#10597273 | 2 |
| C2×#10597278 | 2 |
| C23×C8×C19 | 2 |
| C2×#416 | 19 |