Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625078 | C2 | semidirect |
| 2. #13092995 | C2 | semidirect |
| 3. #13092984 | C2 | semidirect |
| 4. #13092667 | C2 | semidirect |
| 5. #13092660 | C2 | semidirect |
| 6. #13092650 | C2 | semidirect |
| 7. #13092643 | C2 | semidirect |
| 8. #13092459 | C2 | semidirect |
| 9. #13092413 | C2 | semidirect |
| 10. C2×#10625014 | C2 | semidirect |
| 11. C2×C23×AGL(1,ℤ/8) | C2 | semidirect |
| 20. #10625117 | C22 | semidirect |
| 25. #10625109 | C22 | semidirect |
| 33. C2×#67262 | C22 | semidirect |
| 34. C2×C8×D23 | C22 | semidirect |
| 35. #10625017 | C22 | semidirect |
| 36. #10625017 | C22 | semidirect |
| 39. #10625014 | C22 | semidirect |
| 40. #10625014 | C22 | semidirect |
| 41. #10625000 | C22 | semidirect |
| 42. #10624999 | C22 | semidirect |
| 67. M16×C23 | D4 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D23 | semidirect |
| 194. C23 | #3062 | semidirect |
| 220. M16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625078 | 2 |
| #13092995 | 2 |
| #13092984 | 2 |
| #13092667 | 2 |
| #13092660 | 2 |
| #13092650 | 2 |
| #13092643 | 2 |
| #13092459 | 2 |
| #13092413 | 2 |
| C2×#10625014 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #3062 | 23 |