Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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. Q8×#11717581 | C2 | semidirect |
| 3. #20266039 | C2 | semidirect |
| 4. Q8⋊#11717581 | C2 | semidirect |
| 6. C8×#11717581 | C2 | semidirect |
| 31. #13108061 | C8 | semidirect |
| 43. Q8×C101 | C2×C8 | semidirect |
| 58. #11717581 | SD16 | semidirect |
| 60. #11717579 | C2×C8 | semidirect |
| 78. C101 | C8×SD16 | semidirect |
| 121. Q8 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11717581 | 2 |
| #20266205 | 2 |
| #20266039 | 2 |
| Q8⋊#11717581 | 2 |
| #20266025 | 2 |
| C8×#11717581 | 2 |
| #20265262 | 2 |
| C8×SD16 | 101 |