Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. #20261269 | C2 | semidirect |
| 2. C2×C4×D388 | C2 | semidirect |
| 3. #20261066 | C2 | semidirect |
| 4. #20261049 | C2 | semidirect |
| 5. #20261036 | C2 | semidirect |
| 6. #20260951 | C2 | semidirect |
| 7. #20260888 | C2 | semidirect |
| 9. #20260848 | C2 | semidirect |
| 10. #20260837 | C2 | semidirect |
| 11. #432×C97 | C2 | semidirect |
| 17. #15690802 | C22 | semidirect |
| 18. #15690798 | C22 | semidirect |
| 22. C4×Dic194 | C22 | semidirect |
| 27. C4×D388 | C22 | semidirect |
| 32. #15690744 | C22 | semidirect |
| 33. #15690742 | C22 | semidirect |
| 34. #15690735 | C22 | semidirect |
| 37. #15690732 | C22 | semidirect |
| 39. C4⋊C8×C97 | C22 | semidirect |
| 42. #97×C97 | C22 | semidirect |
| 141. C97 | #3114 | semidirect |
| 152. #432 | D97 | semidirect |
| 176. C4⋊C8 | C2×D97 | semidirect |
| 183. #97 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261269 | 2 |
| C2×C4×D388 | 2 |
| #20261066 | 2 |
| #20261049 | 2 |
| #20261036 | 2 |
| #20260951 | 2 |
| #20260888 | 2 |
| #20260871 | 2 |
| #20260848 | 2 |
| #20260837 | 2 |
| #432×C97 | 2 |
| #3114 | 97 |