Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
406 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20261786 | C2 | semidirect |
| 2. #20261765 | C2 | semidirect |
| 3. #20261763 | C2 | semidirect |
| 4. #20261758 | C2 | semidirect |
| 5. #20261757 | C2 | semidirect |
| 6. C4×#13095521 | C2 | semidirect |
| 7. #20261694 | C2 | semidirect |
| 73. D388 | M16 | semidirect |
| 82. #11715897 | #41 | semidirect |
| 105. C97 | #2970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261786 | 2 |
| #20261765 | 2 |
| #20261763 | 2 |
| #20261758 | 2 |
| #20261757 | 2 |
| C4×#13095521 | 2 |
| #20261694 | 2 |
| C4×#13095512 | 2 |
| #2970 | 97 |