Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261445 | C2 | semidirect |
| 3. #20261082 | C2 | semidirect |
| 4. #20261055 | C2 | semidirect |
| 5. #20261025 | C2 | semidirect |
| 6. #20260967 | C2 | semidirect |
| 7. #20260935 | C2 | semidirect |
| 8. #20260884 | C2 | semidirect |
| 9. C8×D388 | C2 | semidirect |
| 10. #102×D97 | C2 | semidirect |
| 11. C4×SD16×C97 | C2 | semidirect |
| 14. C2×#13095498 | C22 | semidirect |
| 15. C2×C8×D97 | C22 | semidirect |
| 16. #15690810 | C22 | semidirect |
| 20. #15690786 | C22 | semidirect |
| 26. C4⋊C4×D97 | C22 | semidirect |
| 27. #15690741 | C22 | semidirect |
| 28. C4⋊#11715895 | C22 | semidirect |
| 29. #15690732 | C22 | semidirect |
| 30. #15690732 | C22 | semidirect |
| 32. #15690730 | C22 | semidirect |
| 33. #15690722 | C22 | semidirect |
| 35. C4×Q8×C97 | C22 | semidirect |
| 37. #106×C97 | C22 | semidirect |
| 38. #103×C97 | C22 | semidirect |
| 40. C4×C8×C97 | C22 | semidirect |
| 102. D388 | SD16 | semidirect |
| 137. C97 | #3295 | semidirect |
| 146. C4×SD16 | D97 | semidirect |
| 162. C4×Q8 | C2×D97 | semidirect |
| 168. #106 | C2×D97 | semidirect |
| 170. #103 | C2×D97 | semidirect |
| 177. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261445 | 2 |
| D4×D388 | 2 |
| #20261082 | 2 |
| #20261055 | 2 |
| #20261025 | 2 |
| #20260967 | 2 |
| #20260935 | 2 |
| #20260884 | 2 |
| C8×D388 | 2 |
| #102×D97 | 2 |
| C4×SD16×C97 | 2 |
| #3295 | 97 |