Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10597436 | C2 | semidirect |
| 2. #11927342 | C2 | semidirect |
| 3. #11927115 | C2 | semidirect |
| 4. #11926725 | C2 | semidirect |
| 5. #11926715 | C2 | semidirect |
| 6. #11926561 | C2 | semidirect |
| 7. #11926560 | C2 | semidirect |
| 8. C2×#10597281 | C2 | semidirect |
| 9. C19×#575 | C2 | semidirect |
| 24. C19×#137 | C22 | semidirect |
| 26. C19×AGL(1,ℤ/8) | C22 | semidirect |
| 32. #10597390 | C22 | semidirect |
| 33. #10597388 | C22 | semidirect |
| 34. #10597382 | C22 | semidirect |
| 36. #10597378 | C22 | semidirect |
| 40. #10597294 | C22 | semidirect |
| 41. #10597282 | C22 | semidirect |
| 42. #10597281 | C22 | semidirect |
| 181. #575 | D19 | semidirect |
| 211. #137 | C2×D19 | semidirect |
| 215. AGL(1,ℤ/8) | C2×D19 | semidirect |
| 228. C19 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597436 | 2 |
| #11927342 | 2 |
| #11927115 | 2 |
| #11926725 | 2 |
| #11926715 | 2 |
| #11926561 | 2 |
| #11926560 | 2 |
| C2×#10597281 | 2 |
| C19×#575 | 2 |
| #3020 | 19 |