Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 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×SD16×D23 | C2 | semidirect |
| 2. C4⋊Q8×D23 | C2 | semidirect |
| 4. #13092791 | C2 | semidirect |
| 5. #13092790 | C2 | semidirect |
| 6. #13092789 | C2 | semidirect |
| 7. #13092788 | C2 | semidirect |
| 8. C4×C8×D23 | C2 | semidirect |
| 9. C23×#492 | C2 | semidirect |
| 13. C2×SD16×C23 | C22 | semidirect |
| 14. C23×C4⋊Q8 | C22 | semidirect |
| 16. #10625115 | C22 | semidirect |
| 17. C2×#67274 | C22 | semidirect |
| 20. C2×#67273 | C22 | semidirect |
| 22. C2×#67263 | C22 | semidirect |
| 28. #10625040 | C22 | semidirect |
| 29. C4×C8×C23 | C22 | semidirect |
| 30. C8×Dic23 | C22 | semidirect |
| 31. C4×C23⋊C8 | C22 | semidirect |
| 60. C8×D23 | D4 | semidirect |
| 80. C4×D23 | SD16 | semidirect |
| 84. C8×C23 | C2×D4 | semidirect |
| 85. C23⋊C8 | C2×D4 | semidirect |
| 96. C4×C23 | C2×SD16 | semidirect |
| 100. Dic23 | C2×SD16 | semidirect |
| 108. #492 | D23 | direct (N × H) |
| 114. D23 | #492 | direct (N × H) |
| 122. C2×SD16 | C2×D23 | semidirect |
| 127. C4⋊Q8 | C2×D23 | semidirect |
| 136. C4×C8 | C2×D23 | semidirect |
| 137. C23 | C2×#492 | semidirect |
| 191. C8 | D4×D23 | semidirect |
| 204. C4 | SD16×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×D23 | 2 |
| C4⋊Q8×D23 | 2 |
| #127×D23 | 2 |
| #13092791 | 2 |
| #13092790 | 2 |
| #13092789 | 2 |
| #13092788 | 2 |
| C4×C8×D23 | 2 |
| C23×#492 | 2 |
| C2×#492 | 23 |