Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 21. #13095495 | C8 | semidirect |
| 29. M16×C97 | C8 | semidirect |
| 67. C97 | #1278 | semidirect |
| 88. M16 | #11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261751 | 2 |
| C2×C4×#11715897 | 2 |
| M16×Dic97 | 2 |
| #1278 | 97 |