Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692263 | C2 | semidirect |
| 3. #20265758 | C2 | semidirect |
| 4. #20265755 | C2 | semidirect |
| 5. #20265426 | C2 | semidirect |
| 6. #20265422 | C2 | semidirect |
| 7. #20265417 | C2 | semidirect |
| 8. #20265412 | C2 | semidirect |
| 9. C2×#15692188 | C2 | semidirect |
| 10. #20265179 | C2 | semidirect |
| 11. #417×C101 | C2 | semidirect |
| 63. C2×#11717579 | D4 | semidirect |
| 153. C101 | #3061 | semidirect |
| 164. #417 | 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×#15692263 | 2 |
| #20265758 | 2 |
| #20265755 | 2 |
| #20265426 | 2 |
| #20265422 | 2 |
| #20265417 | 2 |
| #20265412 | 2 |
| C2×#15692188 | 2 |
| #20265179 | 2 |
| #417×C101 | 2 |
| #3061 | 101 |