Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 51. #11715895 | Q16 | semidirect |
| 64. C97 | #1707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261138 | 2 |
| #20261131 | 2 |
| #20261114 | 2 |
| #20261086 | 2 |
| C8×#11715895 | 2 |
| #487×C97 | 2 |
| #1707 | 97 |