Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4⋊C4×D19 | C2 | semidirect |
| 3. #11926861 | C2 | direct (N × H) |
| 4. C2×#10597274 | C2 | semidirect |
| 5. C2×#10597265 | C2 | semidirect |
| 6. C2×#10597289 | C2 | semidirect |
| 7. C2×(C2×D19)⋊C8 | C2 | semidirect |
| 8. C2×C19×#102 | C2 | semidirect |
| 23. C4⋊C4×D19 | C22 | semidirect |
| 24. C19×#102 | C22 | semidirect |
| 25. #10597289 | C22 | semidirect |
| 26. (C2×D19)⋊C8 | C22 | semidirect |
| 27. #10597274 | C22 | semidirect |
| 28. #10597265 | C22 | semidirect |
| 117. C2×#102 | D19 | semidirect |
| 120. C2×C19 | #481 | semidirect |
| 143. #102 | C2×D19 | semidirect |
| 145. C19 | C2×#481 | semidirect |
| 229. C2 | #11926861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597384 | 2 |
| C2×C4⋊C4×D19 | 2 |
| #11926861 | 2 |
| C2×#10597274 | 2 |
| C2×#10597265 | 2 |
| C2×#10597289 | 2 |
| C2×(C2×D19)⋊C8 | 2 |
| C2×C19×#102 | 2 |
| C2×#481 | 19 |