Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265901 | C2 | semidirect |
| 3. #20265525 | C2 | semidirect |
| 4. #20265503 | C2 | semidirect |
| 5. #20265407 | C2 | semidirect |
| 6. #20265378 | C2 | semidirect |
| 7. #20265342 | C2 | semidirect |
| 8. C4×#13108064 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #20265172 | C2 | semidirect |
| 11. #475×C101 | C2 | semidirect |
| 128. C101 | #3304 | semidirect |
| 133. #475 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265901 | 2 |
| #20265849 | 2 |
| #20265525 | 2 |
| #20265503 | 2 |
| #20265407 | 2 |
| #20265378 | 2 |
| #20265342 | 2 |
| C4×#13108064 | 2 |
| #20265242 | 2 |
| #20265172 | 2 |
| #475×C101 | 2 |
| #3304 | 101 |