Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #20261361 | C2 | direct (N × H) |
| 2. C2×#15690789 | C2 | semidirect |
| 3. C2×#15690787 | C2 | semidirect |
| 6. C22×Dic194 | C22 | semidirect |
| 8. #15690789 | C22 | semidirect |
| 9. #15690787 | C22 | semidirect |
| 10. C2×C4⋊Dic97 | C22 | semidirect |
| 11. C2×#13095490 | C22 | semidirect |
| 20. C2×Dic194 | C23 | semidirect |
| 24. C4⋊Dic97 | C23 | semidirect |
| 25. #13095490 | C23 | semidirect |
| 29. C24×C97 | Q8 | semidirect |
| 43. C23×C97 | C2×Q8 | semidirect |
| 68. C2×C97 | #543 | semidirect |
| 72. C97 | C2×#543 | semidirect |
| 92. C24 | Dic194 | semidirect |
| 115. C23 | C2×Dic194 | semidirect |
| 140. C2 | #20261361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261361 | 2 |
| C2×#15690789 | 2 |
| C2×#15690787 | 2 |
| C22×C22⋊Dic97 | 2 |
| C22×C22⋊C4×C97 | 2 |
| C2×#543 | 97 |