Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
262 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20261754 | C2 | semidirect |
| 2. C4×#13095521 | C2 | semidirect |
| 3. D4⋊#11715897 | C2 | semidirect |
| 81. C97 | #1484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261754 | 2 |
| C4×#13095521 | 2 |
| D4⋊#11715897 | 2 |
| #20261283 | 2 |
| #1484 | 97 |