Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. #20261605 | C2 | semidirect |
| 8. D97⋊M16 | C4 | semidirect |
| 13. C2×C4×#87604 | C4 | semidirect |
| 16. #15690769 | C4 | semidirect |
| 20. C4⋊C4×D97 | C4 | semidirect |
| 23. #117×C97 | C4 | semidirect |
| 28. #13095521 | C2×C4 | semidirect |
| 34. C4×#87604 | C2×C4 | semidirect |
| 46. C4⋊Dic97 | C2×C4 | semidirect |
| 53. C4⋊C4×C97 | C2×C4 | semidirect |
| 111. D97 | #339 | semidirect |
| 113. C97 | C2×#339 | semidirect |
| 129. #117 | #87604 | semidirect |
| 159. C4⋊C4 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C22×C4×#87604 | 2 |
| #20261605 | 2 |
| #117×D97 | 2 |
| C2×#339 | 97 |