Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #20265887 | C2 | semidirect |
| 3. #20265582 | C2 | semidirect |
| 4. #20265517 | C2 | semidirect |
| 5. #20265489 | C2 | semidirect |
| 6. #20265472 | C2 | semidirect |
| 7. #20265467 | C2 | semidirect |
| 8. #20265420 | C2 | semidirect |
| 9. #20265256 | C2 | semidirect |
| 10. #20265216 | C2 | semidirect |
| 11. C4×SD16×C101 | C2 | semidirect |
| 122. C101 | #3357 | semidirect |
| 131. C4×SD16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265892 | 2 |
| #20265887 | 2 |
| #20265582 | 2 |
| #20265517 | 2 |
| #20265489 | 2 |
| #20265472 | 2 |
| #20265467 | 2 |
| #20265420 | 2 |
| #20265256 | 2 |
| #20265216 | 2 |
| C4×SD16×C101 | 2 |
| #3357 | 101 |