Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 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×D97 | C2 | semidirect |
| 2. C2×SD16×D97 | C2 | semidirect |
| 4. #124×D97 | C2 | semidirect |
| 5. #20261120 | C2 | semidirect |
| 6. #20261119 | C2 | semidirect |
| 7. #20261118 | C2 | semidirect |
| 8. #20261117 | C2 | semidirect |
| 9. #20261116 | C2 | semidirect |
| 10. C4×C8×D97 | C2 | semidirect |
| 11. #495×C97 | C2 | semidirect |
| 14. C2×Dic388 | C22 | semidirect |
| 15. C2×#13095501 | C22 | semidirect |
| 17. C2×#13095500 | C22 | semidirect |
| 18. C2×#13095499 | C22 | semidirect |
| 19. C2×#13095498 | C22 | semidirect |
| 26. #15690799 | C22 | semidirect |
| 27. #15690798 | C22 | semidirect |
| 28. #15690797 | C22 | semidirect |
| 32. C4×#11715895 | C22 | semidirect |
| 33. C8×Dic97 | C22 | semidirect |
| 34. C8×Dic97 | C22 | semidirect |
| 35. C2×Q16×C97 | C22 | semidirect |
| 36. C2×SD16×C97 | C22 | semidirect |
| 38. #124×C97 | C22 | semidirect |
| 39. C4×C8×C97 | C22 | semidirect |
| 125. D97 | #495 | direct (N × H) |
| 127. C97 | C2×#495 | semidirect |
| 137. #495 | D97 | direct (N × H) |
| 144. C2×Q16 | C2×D97 | semidirect |
| 149. C2×SD16 | C2×D97 | semidirect |
| 160. #124 | C2×D97 | semidirect |
| 166. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C2×SD16×D97 | 2 |
| C2×D8×D97 | 2 |
| #124×D97 | 2 |
| #20261120 | 2 |
| #20261119 | 2 |
| #20261118 | 2 |
| #20261117 | 2 |
| #20261116 | 2 |
| C4×C8×D97 | 2 |
| #495×C97 | 2 |
| C2×#495 | 97 |