Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. #20261599 | C2 | semidirect |
| 37. #11715895 | M16 | semidirect |
| 54. C97 | #1567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261739 | 2 |
| #20261599 | 2 |
| C4×C8×D97 | 2 |
| #1567 | 97 |