Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 12. #15690877 | C4 | semidirect |
| 14. #15690865 | C4 | semidirect |
| 78. #11715897 | C4⋊C4 | semidirect |
| 104. C97 | #1771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690877 | 2 |
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| C4⋊C4×Dic97 | 2 |
| #1771 | 97 |