Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #20265199 | C2 | semidirect |
| 3. C4×#13108057 | C2 | semidirect |
| 4. Q8⋊#11717579 | C2 | semidirect |
| 5. #20264906 | C2 | semidirect |
| 6. #20264904 | C2 | semidirect |
| 7. Q8⋊C8×C101 | C2 | semidirect |
| 61. Q8×C101 | M16 | semidirect |
| 73. D404 | M16 | semidirect |
| 111. C101 | #1489 | semidirect |
| 116. Q8⋊C8 | D101 | semidirect |
| 172. Q8 | #13108057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13108075 | 2 |
| #20265199 | 2 |
| C4×#13108057 | 2 |
| Q8⋊#11717579 | 2 |
| #20264906 | 2 |
| #20264904 | 2 |
| Q8⋊C8×C101 | 2 |
| #1489 | 101 |