Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 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. C4⋊Q8×D23 | C2 | semidirect |
| 3. #13092765 | C2 | semidirect |
| 4. #13092764 | C2 | semidirect |
| 5. #13092763 | C2 | semidirect |
| 6. #13092762 | C2 | semidirect |
| 7. #102×D23 | C2 | semidirect |
| 8. C4×C8×D23 | C2 | semidirect |
| 9. C23×#486 | C2 | semidirect |
| 14. C23×C4⋊Q8 | C22 | semidirect |
| 24. #10625059 | C22 | semidirect |
| 27. #10625040 | C22 | semidirect |
| 28. C23×#102 | C22 | semidirect |
| 29. C4×C8×C23 | C22 | semidirect |
| 30. #10625014 | C22 | semidirect |
| 31. #10625003 | C22 | semidirect |
| 32. C8×Dic23 | C22 | semidirect |
| 33. #10624991 | C22 | semidirect |
| 34. C4×C23⋊C8 | C22 | semidirect |
| 127. #486 | D23 | direct (N × H) |
| 135. D23 | #486 | direct (N × H) |
| 145. C4⋊Q8 | C2×D23 | semidirect |
| 157. #102 | C2×D23 | semidirect |
| 160. C4×C8 | C2×D23 | semidirect |
| 161. C23 | C2×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D23 | 2 |
| #127×D23 | 2 |
| #13092765 | 2 |
| #13092764 | 2 |
| #13092763 | 2 |
| #13092762 | 2 |
| #102×D23 | 2 |
| C4×C8×D23 | 2 |
| C23×#486 | 2 |
| C2×#486 | 23 |