Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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. C2×#10625161 | C2 | semidirect |
| 2. C22×#67273 | C2 | semidirect |
| 3. #13092984 | C2 | semidirect |
| 4. #13092559 | C2 | semidirect |
| 5. #13092554 | C2 | semidirect |
| 6. #13092427 | C2 | semidirect |
| 7. #13092413 | C2 | semidirect |
| 8. #13092385 | C2 | semidirect |
| 9. C2×C23×AGL(1,ℤ/8) | C2 | semidirect |
| 14. C2×Q8×D23 | C22 | semidirect |
| 16. C2×#67290 | C22 | semidirect |
| 33. #10625017 | C22 | semidirect |
| 34. #10625014 | C22 | semidirect |
| 35. (C2×D23)⋊C8 | C22 | semidirect |
| 36. #10624998 | C22 | semidirect |
| 39. #41×C23 | D4 | semidirect |
| 70. C2×Dic46 | D4 | semidirect |
| 141. C2×AGL(1,ℤ/8) | D23 | semidirect |
| 182. C23 | #3010 | semidirect |
| 191. #41 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625161 | 2 |
| C22×#67273 | 2 |
| #13092984 | 2 |
| #13092559 | 2 |
| #13092554 | 2 |
| #13092427 | 2 |
| #13092413 | 2 |
| #13092385 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #3010 | 23 |