Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20265900 | C2 | semidirect |
| 3. #20265523 | C2 | semidirect |
| 4. #20265500 | C2 | semidirect |
| 5. #20265463 | C2 | semidirect |
| 6. #20265403 | C2 | semidirect |
| 7. #20265336 | C2 | semidirect |
| 8. C4×#13108064 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #20265170 | C2 | semidirect |
| 11. #460×C101 | C2 | semidirect |
| 128. C101 | #3304 | semidirect |
| 135. #460 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265847 | 2 |
| #20265523 | 2 |
| #20265500 | 2 |
| #20265463 | 2 |
| #20265403 | 2 |
| #20265336 | 2 |
| C4×#13108064 | 2 |
| #20265242 | 2 |
| #20265170 | 2 |
| #460×C101 | 2 |
| #3304 | 101 |