Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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×#15692285 | C2 | semidirect |
| 2. C22×#13108063 | C2 | semidirect |
| 4. #20265654 | C2 | semidirect |
| 5. #20265402 | C2 | semidirect |
| 6. #20265376 | C2 | semidirect |
| 7. #20265203 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. #416×C101 | C2 | semidirect |
| 13. C2×#13108064 | C22 | semidirect |
| 16. C2×#13108062 | C22 | semidirect |
| 23. #15692220 | C22 | semidirect |
| 26. #15692184 | C22 | semidirect |
| 31. #103×C101 | C22 | semidirect |
| 32. #102×C101 | C22 | semidirect |
| 36. C2×Dic202 | D4 | semidirect |
| 117. C101 | #3043 | semidirect |
| 126. #416 | D101 | semidirect |
| 147. #103 | C2×D101 | semidirect |
| 149. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| C22×#13108063 | 2 |
| #20265741 | 2 |
| #20265654 | 2 |
| #20265402 | 2 |
| #20265376 | 2 |
| #20265203 | 2 |
| #20265181 | 2 |
| #416×C101 | 2 |
| #3043 | 101 |