Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261363 | C2 | semidirect |
| 3. #20261037 | C2 | semidirect |
| 4. #20261033 | C2 | semidirect |
| 5. #20261023 | C2 | semidirect |
| 6. #20261013 | C2 | semidirect |
| 7. #20260777 | C2 | semidirect |
| 8. #20260771 | C2 | semidirect |
| 9. #20260763 | C2 | semidirect |
| 14. #15690809 | C22 | semidirect |
| 16. #15690801 | C22 | semidirect |
| 26. #15690744 | C22 | semidirect |
| 27. #15690743 | C22 | semidirect |
| 28. #15690743 | C22 | semidirect |
| 29. #15690742 | C22 | semidirect |
| 30. #15690741 | C22 | semidirect |
| 31. #15690741 | C22 | semidirect |
| 32. #15690739 | C22 | semidirect |
| 33. #15690739 | C22 | semidirect |
| 66. C2×D4×C97 | Q8 | semidirect |
| 125. C97 | #3081 | semidirect |
| 170. C2×D4 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261210 | 2 |
| #20261037 | 2 |
| #20261033 | 2 |
| #20261023 | 2 |
| #20261013 | 2 |
| #20260777 | 2 |
| #20260771 | 2 |
| #20260763 | 2 |
| C2×#15690731 | 2 |
| #418×C97 | 2 |
| #3081 | 97 |