Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692275 | C2 | semidirect |
| 2. C2×#15692262 | C2 | semidirect |
| 3. #20265755 | C2 | semidirect |
| 4. #20265425 | C2 | semidirect |
| 5. #20265421 | C2 | semidirect |
| 6. #20265416 | C2 | semidirect |
| 7. #20265411 | C2 | semidirect |
| 8. C2×#15692188 | C2 | semidirect |
| 9. #20265178 | C2 | semidirect |
| 10. #20265176 | C2 | semidirect |
| 11. #537×C101 | C2 | semidirect |
| 58. C2×#11717579 | D4 | semidirect |
| 153. C101 | #3061 | semidirect |
| 157. #537 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692275 | 2 |
| C2×#15692262 | 2 |
| #20265755 | 2 |
| #20265425 | 2 |
| #20265421 | 2 |
| #20265416 | 2 |
| #20265411 | 2 |
| C2×#15692188 | 2 |
| #20265178 | 2 |
| #20265176 | 2 |
| #537×C101 | 2 |
| #3061 | 101 |