Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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 |
|---|---|---|
| 1. C2×#10597378 | C2 | semidirect |
| 2. C22×#64525 | C2 | semidirect |
| 3. #11927113 | C2 | semidirect |
| 4. #11926759 | C2 | semidirect |
| 5. #11926739 | C2 | semidirect |
| 6. #11926571 | C2 | semidirect |
| 7. #11926548 | C2 | semidirect |
| 8. #11926538 | C2 | semidirect |
| 9. C19×#518 | C2 | semidirect |
| 14. C4×D4×C19 | C22 | semidirect |
| 18. C2×#64526 | C22 | semidirect |
| 22. C2×#64525 | C22 | semidirect |
| 27. #10597321 | C22 | semidirect |
| 28. #10597320 | C22 | semidirect |
| 29. #10597267 | C22 | semidirect |
| 30. #10597266 | C22 | semidirect |
| 31. #10597266 | C22 | semidirect |
| 32. C4⋊(C19⋊C8) | C22 | semidirect |
| 37. C2×D4×C19 | D4 | semidirect |
| 119. #518 | D19 | semidirect |
| 146. C4×D4 | C2×D19 | semidirect |
| 154. C19 | #3041 | semidirect |
| 169. C2×D4 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597378 | 2 |
| C22×#64525 | 2 |
| #11927113 | 2 |
| #11926759 | 2 |
| #11926739 | 2 |
| #11926571 | 2 |
| #11926548 | 2 |
| #11926538 | 2 |
| C19×#518 | 2 |
| #3041 | 19 |