Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 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. #11927172 | C2 | semidirect |
| 2. #11926844 | C2 | semidirect |
| 3. #11926844 | C2 | semidirect |
| 4. #11926834 | C2 | semidirect |
| 5. #11926824 | C2 | semidirect |
| 6. #11926587 | C2 | semidirect |
| 7. #11926580 | C2 | semidirect |
| 8. #11926571 | C2 | semidirect |
| 27. #10597316 | C22 | semidirect |
| 28. #10597315 | C22 | semidirect |
| 33. #10597265 | C22 | semidirect |
| 34. #10597265 | C22 | semidirect |
| 35. #10597265 | C22 | semidirect |
| 36. #10597264 | C22 | semidirect |
| 37. #10597264 | C22 | semidirect |
| 38. #10597264 | C22 | semidirect |
| 39. C4⋊(C19⋊C8) | C22 | semidirect |
| 40. C4⋊(C19⋊C8) | C22 | semidirect |
| 44. C2×D4×C19 | Q8 | semidirect |
| 165. C19 | #3081 | semidirect |
| 170. C2×D4 | Dic38 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927172 | 2 |
| #11926844 | 2 |
| #11926834 | 2 |
| #11926824 | 2 |
| #11926587 | 2 |
| #11926580 | 2 |
| #11926571 | 2 |
| #11926549 | 2 |
| C2×#10597289 | 2 |
| C19×#518 | 2 |
| #3081 | 19 |