Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #13093215 | C2 | semidirect |
| 2. C2×#10625103 | C2 | semidirect |
| 3. #13093184 | C2 | semidirect |
| 4. #13092685 | C2 | semidirect |
| 5. #13092678 | C2 | semidirect |
| 6. #13092465 | C2 | semidirect |
| 7. #13092399 | C2 | semidirect |
| 8. C2×#10625015 | C2 | semidirect |
| 9. C2×C23×AGL(1,ℤ/8) | C2 | semidirect |
| 18. #10625122 | C22 | semidirect |
| 20. #10625120 | C22 | semidirect |
| 22. #10625119 | C22 | semidirect |
| 24. C2×#67273 | C22 | semidirect |
| 28. C2×#67272 | C22 | semidirect |
| 33. #10625015 | C22 | semidirect |
| 34. #10625006 | C22 | semidirect |
| 35. #10625005 | C22 | semidirect |
| 36. #10625004 | C22 | semidirect |
| 143. C2×AGL(1,ℤ/8) | D23 | semidirect |
| 184. C23 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093215 | 2 |
| C2×#10625103 | 2 |
| #13093184 | 2 |
| #13092685 | 2 |
| #13092678 | 2 |
| #13092465 | 2 |
| #13092399 | 2 |
| C2×#10625015 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #3068 | 23 |