Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 55. #11717581 | Q16 | semidirect |
| 72. C101 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266228 | 2 |
| #20266227 | 2 |
| #20266041 | 2 |
| #20266027 | 2 |
| Q8⋊#11717581 | 2 |
| C8×#11717581 | 2 |
| #20265269 | 2 |
| #1591 | 101 |