Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#15692288 | C2 | semidirect |
| 3. #20265748 | C2 | semidirect |
| 4. #20265435 | C2 | semidirect |
| 5. #20265423 | C2 | semidirect |
| 6. #20265418 | C2 | semidirect |
| 7. #20265406 | C2 | semidirect |
| 8. #20265219 | C2 | semidirect |
| 9. #20265174 | C2 | semidirect |
| 10. C2×#15692180 | C2 | semidirect |
| 11. C2×#131×C101 | C2 | semidirect |
| 79. M16×C101 | D4 | semidirect |
| 144. C101 | #3063 | semidirect |
| 146. C2×#131 | D101 | semidirect |
| 210. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| #20265755 | 2 |
| #20265748 | 2 |
| #20265435 | 2 |
| #20265423 | 2 |
| #20265418 | 2 |
| #20265406 | 2 |
| #20265219 | 2 |
| #20265174 | 2 |
| C2×#15692180 | 2 |
| C2×#131×C101 | 2 |
| #3063 | 101 |