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×#10625085 | C2 | semidirect |
| 2. #13092968 | C2 | semidirect |
| 3. #127×D23 | C2 | semidirect |
| 4. #13092803 | C2 | semidirect |
| 5. #13092794 | C2 | semidirect |
| 6. #13092793 | C2 | semidirect |
| 7. #13092791 | C2 | semidirect |
| 8. C4×#67262 | C2 | semidirect |
| 9. C23×#492 | C2 | semidirect |
| 13. C2×SD16×C23 | C22 | semidirect |
| 14. C23×C4⋊Q8 | C22 | semidirect |
| 16. #10625118 | C22 | semidirect |
| 17. C2×#67274 | C22 | semidirect |
| 20. C2×#67272 | C22 | semidirect |
| 22. C2×D184 | C22 | semidirect |
| 27. #10625045 | 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 |
| 99. C4×C23 | AGL(1,ℤ/8) | semidirect |
| 110. #492 | D23 | semidirect |
| 123. C2×SD16 | C2×D23 | semidirect |
| 127. C4⋊Q8 | C2×D23 | semidirect |
| 139. C4×C8 | C2×D23 | semidirect |
| 140. C23 | #3151 | semidirect |
| 195. C8 | D4×D23 | semidirect |
| 209. C4 | #10625085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625085 | 2 |
| #13092968 | 2 |
| #127×D23 | 2 |
| #13092803 | 2 |
| #13092794 | 2 |
| #13092793 | 2 |
| #13092791 | 2 |
| C4×#67262 | 2 |
| C23×#492 | 2 |
| #3151 | 23 |