Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #20261290 | C2 | semidirect |
| 3. #20261098 | C2 | semidirect |
| 4. #20261083 | C2 | semidirect |
| 5. #20261082 | C2 | semidirect |
| 6. #20261081 | C2 | semidirect |
| 7. #20260738 | C2 | semidirect |
| 8. C4×#13095494 | C2 | semidirect |
| 9. #486×C97 | C2 | semidirect |
| 14. #15690810 | C22 | semidirect |
| 19. #15690801 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 27. #15690731 | C22 | semidirect |
| 28. #15690730 | C22 | semidirect |
| 29. #15690720 | C22 | semidirect |
| 30. C4×#11715895 | C22 | semidirect |
| 31. C4⋊Q8×C97 | C22 | semidirect |
| 33. #102×C97 | C22 | semidirect |
| 34. C4×C8×C97 | C22 | semidirect |
| 124. C97 | #3138 | semidirect |
| 131. #486 | D97 | semidirect |
| 139. C4⋊Q8 | C2×D97 | semidirect |
| 155. #102 | C2×D97 | semidirect |
| 158. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| #127×D97 | 2 |
| #20261098 | 2 |
| #20261083 | 2 |
| #20261082 | 2 |
| #20261081 | 2 |
| #20260738 | 2 |
| C4×#13095494 | 2 |
| #486×C97 | 2 |
| #3138 | 97 |