Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265897 | C2 | semidirect |
| 2. #20265523 | C2 | semidirect |
| 3. #20265498 | C2 | semidirect |
| 4. #20265462 | C2 | semidirect |
| 5. #20265404 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265339 | C2 | semidirect |
| 8. C4×#13108064 | C2 | semidirect |
| 9. D4×#11717579 | C2 | semidirect |
| 10. #20265173 | C2 | semidirect |
| 128. C101 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265897 | 2 |
| #20265523 | 2 |
| #20265498 | 2 |
| #20265462 | 2 |
| #20265404 | 2 |
| #20265374 | 2 |
| #20265339 | 2 |
| C4×#13108064 | 2 |
| D4×#11717579 | 2 |
| #20265173 | 2 |
| #550×C101 | 2 |
| #3304 | 101 |