Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #20261388 | C2 | semidirect |
| 2. #20261370 | C2 | semidirect |
| 3. #20261047 | C2 | semidirect |
| 4. #20261012 | C2 | semidirect |
| 5. #20260970 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260870 | C2 | semidirect |
| 8. C4×D776 | C2 | semidirect |
| 9. C8×D388 | C2 | semidirect |
| 10. #102×D97 | C2 | semidirect |
| 11. #486×C97 | C2 | semidirect |
| 16. C2×#13095496 | C22 | semidirect |
| 17. C2×C8×D97 | C22 | semidirect |
| 20. #15690785 | C22 | semidirect |
| 26. C4×D388 | C22 | semidirect |
| 27. C4⋊C4×D97 | C22 | semidirect |
| 28. #15690744 | C22 | semidirect |
| 29. #15690743 | C22 | semidirect |
| 30. C4⋊#11715895 | C22 | semidirect |
| 32. #15690732 | 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 |
| 103. D388 | D8 | semidirect |
| 104. D388 | #41 | semidirect |
| 143. C97 | #3294 | semidirect |
| 146. #486 | D97 | semidirect |
| 161. C4⋊Q8 | C2×D97 | semidirect |
| 180. #102 | C2×D97 | semidirect |
| 181. #102 | C2×D97 | semidirect |
| 183. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261388 | 2 |
| #20261370 | 2 |
| #20261047 | 2 |
| #20261012 | 2 |
| #20260970 | 2 |
| #20260927 | 2 |
| #20260870 | 2 |
| C4×D776 | 2 |
| C8×D388 | 2 |
| #102×D97 | 2 |
| #486×C97 | 2 |
| #3294 | 97 |