Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#15690843 | C2 | semidirect |
| 3. C2×#15690798 | C2 | semidirect |
| 4. C4×#13095511 | C2 | semidirect |
| 5. #20260958 | C2 | semidirect |
| 6. #20260951 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 8. #20260741 | C2 | semidirect |
| 9. #423×C97 | C2 | semidirect |
| 15. C2×Dic388 | C22 | semidirect |
| 17. C2×#13095500 | C22 | semidirect |
| 22. C4×Dic194 | C22 | semidirect |
| 23. C4×D388 | C22 | semidirect |
| 29. #15690735 | C22 | semidirect |
| 34. C4⋊C8×C97 | C22 | semidirect |
| 126. C97 | #3040 | semidirect |
| 133. #423 | 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 |
|---|---|
| C2×#15690843 | 2 |
| C2×#15690838 | 2 |
| C2×#15690798 | 2 |
| C4×#13095511 | 2 |
| #20260958 | 2 |
| #20260951 | 2 |
| #20260745 | 2 |
| #20260741 | 2 |
| #423×C97 | 2 |
| #3040 | 97 |