Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20261759 | C2 | direct (N × H) |
| 2. C2×#15690877 | C2 | semidirect |
| 3. C2×C4⋊#11715897 | C2 | semidirect |
| 6. C2×#15690865 | C2 | semidirect |
| 7. C2×C4×#11715897 | C2 | semidirect |
| 13. #15690877 | C22 | semidirect |
| 14. C4⋊#11715897 | C22 | semidirect |
| 17. #15690865 | C22 | semidirect |
| 18. C4×#11715897 | C22 | semidirect |
| 98. C2×C97 | #433 | semidirect |
| 103. C97 | C2×#433 | semidirect |
| 201. C2 | #20261759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261759 | 2 |
| C2×#15690877 | 2 |
| C2×C4⋊#11715897 | 2 |
| C2×C22⋊#11715897 | 2 |
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| C2×#15690766 | 2 |
| C2×#433 | 97 |