Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#13095499 | C2 | semidirect |
| 2. C2×#15690789 | C2 | semidirect |
| 3. #20260886 | C2 | direct (N × H) |
| 4. C2×#15690731 | C2 | semidirect |
| 5. C2×C22⋊#11715895 | C2 | semidirect |
| 7. C22×Dic194 | C22 | semidirect |
| 9. C2×#13095499 | C22 | semidirect |
| 10. C22×#11715895 | C22 | semidirect |
| 12. #15690789 | C22 | semidirect |
| 13. C2×C4⋊Dic97 | C22 | semidirect |
| 16. #15690731 | C22 | semidirect |
| 17. C22⋊#11715895 | C22 | semidirect |
| 27. C2×Dic194 | C23 | semidirect |
| 32. C2×#11715895 | C23 | semidirect |
| 34. C4⋊Dic97 | C23 | semidirect |
| 66. C23×C97 | SD16 | semidirect |
| 97. C22×C97 | C2×SD16 | semidirect |
| 107. C2×C97 | #450 | semidirect |
| 112. C97 | C2×#450 | semidirect |
| 178. C23 | #13095499 | semidirect |
| 209. C22 | C2×#13095499 | semidirect |
| 219. C2 | #20260886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095499 | 2 |
| C2×#15690789 | 2 |
| #20260886 | 2 |
| C2×#15690731 | 2 |
| C2×C22⋊#11715895 | 2 |
| C23×D4×C97 | 2 |
| C2×#450 | 97 |