Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20261537 | C2 | semidirect |
| 2. #20261172 | C2 | semidirect |
| 3. #20261170 | C2 | semidirect |
| 4. #20261168 | C2 | semidirect |
| 5. C2×D1552 | C2 | semidirect |
| 6. D16×D97 | C2 | semidirect |
| 7. #20261151 | C2 | semidirect |
| 8. #508×C97 | C2 | semidirect |
| 12. #15690833 | C22 | semidirect |
| 13. C2×D776 | C22 | semidirect |
| 14. D8×D97 | C22 | semidirect |
| 16. #15690753 | C22 | semidirect |
| 17. D1552 | C22 | semidirect |
| 18. D1552 | C22 | semidirect |
| 19. #15690751 | C22 | semidirect |
| 20. #15690750 | C22 | semidirect |
| 21. #15690749 | C22 | semidirect |
| 22. C16×D97 | C22 | semidirect |
| 23. #135×C97 | C22 | semidirect |
| 24. Q32×C97 | C22 | semidirect |
| 25. SD32×C97 | C22 | semidirect |
| 26. D16×C97 | C22 | semidirect |
| 27. C2×C16×C97 | C22 | semidirect |
| 85. C97 | #3415 | semidirect |
| 90. #508 | D97 | semidirect |
| 98. #135 | C2×D97 | semidirect |
| 102. Q32 | C2×D97 | semidirect |
| 104. SD32 | C2×D97 | semidirect |
| 108. D16 | C2×D97 | semidirect |
| 112. C2×C16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261537 | 2 |
| #20261172 | 2 |
| #20261170 | 2 |
| #20261168 | 2 |
| C2×D1552 | 2 |
| D16×D97 | 2 |
| #20261151 | 2 |
| #508×C97 | 2 |
| #3415 | 97 |