Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#10625079 | C2 | semidirect |
| 2. C2×#10625121 | C2 | semidirect |
| 3. C22×#67272 | C2 | semidirect |
| 4. #13092984 | C2 | semidirect |
| 5. #13092981 | C2 | semidirect |
| 6. #13092805 | C2 | semidirect |
| 7. #13092803 | C2 | semidirect |
| 8. #13092798 | C2 | semidirect |
| 9. #13092792 | C2 | semidirect |
| 10. #13092375 | C2 | semidirect |
| 11. C2×C23×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×SD16×C23 | C22 | semidirect |
| 18. C2×D8×C23 | C22 | semidirect |
| 22. #10625118 | C22 | semidirect |
| 23. C2×#67275 | C22 | semidirect |
| 24. C2×#67274 | C22 | semidirect |
| 25. #10625111 | C22 | semidirect |
| 26. #10625111 | C22 | semidirect |
| 29. #10625107 | C22 | semidirect |
| 30. C2×#67273 | C22 | semidirect |
| 34. C2×#67272 | C22 | semidirect |
| 39. C2×D184 | C22 | semidirect |
| 40. C2×#67263 | C22 | semidirect |
| 41. #10624997 | C22 | semidirect |
| 42. C8×Dic23 | C22 | semidirect |
| 70. M16×C23 | D4 | semidirect |
| 83. C2×C23⋊C8 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D23 | semidirect |
| 176. C2×SD16 | C2×D23 | semidirect |
| 182. C2×D8 | C2×D23 | semidirect |
| 196. C23 | #3155 | semidirect |
| 232. M16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625079 | 2 |
| C2×#10625121 | 2 |
| C22×#67272 | 2 |
| #13092984 | 2 |
| #13092981 | 2 |
| #13092805 | 2 |
| #13092803 | 2 |
| #13092798 | 2 |
| #13092792 | 2 |
| #13092375 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #3155 | 23 |