Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 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. C2×#10625082 | C2 | semidirect |
| 2. #13092965 | C2 | semidirect |
| 3. #127×D23 | C2 | semidirect |
| 4. #13092805 | C2 | semidirect |
| 5. #13092793 | C2 | semidirect |
| 6. #13092790 | C2 | semidirect |
| 7. #13092789 | C2 | semidirect |
| 8. C4×#67262 | C2 | semidirect |
| 9. C23×#493 | C2 | semidirect |
| 13. C2×D8×C23 | C22 | semidirect |
| 15. C23×#127 | C22 | semidirect |
| 19. #10625107 | C22 | semidirect |
| 21. C2×#67273 | C22 | semidirect |
| 22. C2×#67272 | C22 | semidirect |
| 24. C2×#67263 | C22 | semidirect |
| 28. #10625040 | C22 | semidirect |
| 29. C4×C8×C23 | C22 | semidirect |
| 30. #10624997 | C22 | semidirect |
| 31. C4×C23⋊C8 | C22 | semidirect |
| 60. #67262 | D4 | semidirect |
| 85. C8×C23 | C2×D4 | semidirect |
| 86. C23⋊C8 | C2×D4 | semidirect |
| 98. C4×C23 | AGL(1,ℤ/8) | semidirect |
| 108. #493 | D23 | semidirect |
| 125. C2×D8 | C2×D23 | semidirect |
| 132. #127 | C2×D23 | semidirect |
| 139. C4×C8 | C2×D23 | semidirect |
| 140. C23 | #3151 | semidirect |
| 195. C8 | D4×D23 | semidirect |
| 209. C4 | #10625082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625082 | 2 |
| #13092965 | 2 |
| #127×D23 | 2 |
| #13092805 | 2 |
| #13092793 | 2 |
| #13092790 | 2 |
| #13092789 | 2 |
| C4×#67262 | 2 |
| C23×#493 | 2 |
| #3151 | 23 |