Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #13092783 | C2 | semidirect |
| 3. #13092779 | C2 | semidirect |
| 4. #13092774 | C2 | semidirect |
| 5. #13092765 | C2 | semidirect |
| 6. #13092421 | C2 | semidirect |
| 7. #13092416 | C2 | semidirect |
| 8. #13092411 | C2 | semidirect |
| 9. C2×#10624991 | C2 | semidirect |
| 10. #13092373 | C2 | semidirect |
| 11. C23×#544 | C2 | semidirect |
| 15. C23×C4⋊Q8 | C22 | semidirect |
| 17. C23×#125 | C22 | semidirect |
| 29. #10624992 | C22 | semidirect |
| 30. #10624992 | C22 | semidirect |
| 31. #10624992 | C22 | semidirect |
| 36. #10624991 | C22 | semidirect |
| 37. #10624991 | C22 | semidirect |
| 38. #10624991 | C22 | semidirect |
| 39. #10624985 | C22 | semidirect |
| 40. C4×C23⋊C8 | C22 | semidirect |
| 130. #544 | D23 | semidirect |
| 152. C4⋊Q8 | C2×D23 | semidirect |
| 155. #125 | C2×D23 | semidirect |
| 176. C23 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092986 | 2 |
| #13092783 | 2 |
| #13092779 | 2 |
| #13092774 | 2 |
| #13092765 | 2 |
| #13092421 | 2 |
| #13092416 | 2 |
| #13092411 | 2 |
| C2×#10624991 | 2 |
| #13092373 | 2 |
| C23×#544 | 2 |
| #3136 | 23 |