Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20265900 | C2 | semidirect |
| 2. #20265523 | C2 | semidirect |
| 4. #20264922 | C2 | semidirect |
| 5. Q8⋊#11717579 | C2 | semidirect |
| 6. #20264904 | C2 | semidirect |
| 7. #460×C101 | C2 | semidirect |
| 96. C101 | #1628 | semidirect |
| 99. #460 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265523 | 2 |
| #20265369 | 2 |
| #20264922 | 2 |
| Q8⋊#11717579 | 2 |
| #20264904 | 2 |
| #460×C101 | 2 |
| #1628 | 101 |