Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 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×Q16×D23 | C2 | semidirect |
| 3. C4⋊Q8×D23 | C2 | semidirect |
| 5. #13092812 | C2 | semidirect |
| 6. #13092811 | C2 | semidirect |
| 7. #13092810 | C2 | semidirect |
| 8. #13092809 | C2 | semidirect |
| 9. #13092808 | C2 | semidirect |
| 10. #97×D23 | C2 | semidirect |
| 11. C23×#497 | C2 | semidirect |
| 15. C2×Q16×C23 | C22 | semidirect |
| 17. C23×C4⋊Q8 | C22 | semidirect |
| 20. #10625115 | C22 | semidirect |
| 21. C2×#67275 | C22 | semidirect |
| 22. C2×#67275 | C22 | semidirect |
| 28. C2×Dic92 | C22 | semidirect |
| 37. #10625040 | C22 | semidirect |
| 38. C23×#97 | C22 | semidirect |
| 39. #10624997 | C22 | semidirect |
| 40. #10624985 | C22 | semidirect |
| 136. #497 | D23 | direct (N × H) |
| 142. D23 | #497 | direct (N × H) |
| 150. C2×Q16 | C2×D23 | semidirect |
| 160. C4⋊Q8 | C2×D23 | semidirect |
| 171. #97 | C2×D23 | semidirect |
| 172. C23 | C2×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D23 | 2 |
| C2×SD16×D23 | 2 |
| C4⋊Q8×D23 | 2 |
| #124×D23 | 2 |
| #13092812 | 2 |
| #13092811 | 2 |
| #13092810 | 2 |
| #13092809 | 2 |
| #13092808 | 2 |
| #97×D23 | 2 |
| C23×#497 | 2 |
| C2×#497 | 23 |