Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20265549 | C2 | semidirect |
| 2. #20265472 | C2 | semidirect |
| 3. #20265467 | C2 | semidirect |
| 4. #20264921 | C2 | semidirect |
| 5. Q8⋊#11717579 | C2 | semidirect |
| 6. D4⋊#11717579 | C2 | semidirect |
| 53. Q8×C101 | SD16 | semidirect |
| 99. C101 | #1631 | semidirect |
| 153. Q8 | #13108062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265549 | 2 |
| #20265472 | 2 |
| #20265467 | 2 |
| #20264921 | 2 |
| Q8⋊#11717579 | 2 |
| D4⋊#11717579 | 2 |
| #550×C101 | 2 |
| #1631 | 101 |