Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 3. #20261742 | C2 | direct (N × H) |
| 4. C2×#15690877 | C2 | semidirect |
| 5. C2×C4⋊#11715897 | C2 | semidirect |
| 14. #15690877 | C22 | semidirect |
| 15. C4⋊#11715897 | C22 | semidirect |
| 80. C2×C97 | #424 | semidirect |
| 86. C97 | C2×#424 | semidirect |
| 167. C2 | #20261742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| C22×#13095519 | 2 |
| #20261742 | 2 |
| C2×#15690877 | 2 |
| C2×C4⋊#11715897 | 2 |
| C2×#15690768 | 2 |
| C2×#424 | 97 |