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. #13093183 | C2 | semidirect |
| 4. #13092684 | C2 | semidirect |
| 5. #13092677 | C2 | semidirect |
| 6. #13092466 | C2 | semidirect |
| 7. #13092401 | C2 | semidirect |
| 8. C2×#10625015 | C2 | semidirect |
| 9. C2×C23×AGL(1,ℤ/8) | C2 | semidirect |
| 15. C2×SD16×C23 | C22 | semidirect |
| 16. C2×D8×C23 | C22 | semidirect |
| 21. #10625113 | C22 | semidirect |
| 25. #10625103 | C22 | semidirect |
| 32. #10625072 | C22 | semidirect |
| 33. #10625018 | C22 | semidirect |
| 34. #10625015 | C22 | semidirect |
| 35. #10625015 | C22 | semidirect |
| 36. #10625001 | C22 | semidirect |
| 143. C2×AGL(1,ℤ/8) | D23 | semidirect |
| 170. C2×SD16 | C2×D23 | semidirect |
| 172. C2×D8 | C2×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 |
| #13093183 | 2 |
| #13092684 | 2 |
| #13092677 | 2 |
| #13092466 | 2 |
| #13092401 | 2 |
| C2×#10625015 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #3068 | 23 |