Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20260788 | C2 | semidirect |
| 2. #20260759 | C2 | semidirect |
| 3. D4⋊#11715895 | C2 | semidirect |
| 8. C4⋊#11715895 | C22 | semidirect |
| 10. C4×#11715895 | C22 | semidirect |
| 50. D4×C97 | M16 | semidirect |
| 90. C97 | #1486 | semidirect |
| 140. D4 | #13095495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260788 | 2 |
| #20260759 | 2 |
| D4⋊#11715895 | 2 |
| C2×C4×D4×C97 | 2 |
| #1486 | 97 |