Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261446 | C2 | semidirect |
| 3. #20261052 | C2 | semidirect |
| 4. #20261022 | C2 | semidirect |
| 5. #20260963 | C2 | semidirect |
| 6. #20260932 | C2 | semidirect |
| 7. #20260887 | C2 | semidirect |
| 8. C4×#13095500 | C2 | semidirect |
| 9. C8×D388 | C2 | semidirect |
| 10. #102×D97 | C2 | semidirect |
| 11. #486×C97 | C2 | semidirect |
| 15. C2×#13095499 | C22 | semidirect |
| 16. C2×C8×D97 | C22 | semidirect |
| 18. #15690790 | C22 | semidirect |
| 23. C4×Dic194 | C22 | semidirect |
| 27. C4⋊C4×D97 | C22 | semidirect |
| 28. #15690742 | C22 | semidirect |
| 29. #15690741 | C22 | semidirect |
| 30. C4⋊#11715895 | C22 | semidirect |
| 31. #15690735 | C22 | semidirect |
| 33. #15690731 | C22 | semidirect |
| 35. #15690722 | C22 | semidirect |
| 36. C4⋊Q8×C97 | C22 | semidirect |
| 38. #102×C97 | C22 | semidirect |
| 39. #102×C97 | C22 | semidirect |
| 40. C4×C8×C97 | C22 | semidirect |
| 99. D388 | SD16 | semidirect |
| 137. C97 | #3295 | semidirect |
| 140. #486 | D97 | semidirect |
| 154. C4⋊Q8 | C2×D97 | semidirect |
| 174. #102 | C2×D97 | semidirect |
| 175. #102 | 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 |
|---|---|
| #20261446 | 2 |
| #20261370 | 2 |
| #20261052 | 2 |
| #20261022 | 2 |
| #20260963 | 2 |
| #20260932 | 2 |
| #20260887 | 2 |
| C4×#13095500 | 2 |
| C8×D388 | 2 |
| #102×D97 | 2 |
| #486×C97 | 2 |
| #3295 | 97 |