Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #20265805 | C2 | semidirect |
| 3. #20265544 | C2 | semidirect |
| 4. #20265535 | C2 | semidirect |
| 5. #20265530 | C2 | semidirect |
| 6. #20265526 | C2 | semidirect |
| 7. #20265185 | C2 | semidirect |
| 9. C2×#15692180 | C2 | semidirect |
| 10. #20265132 | C2 | semidirect |
| 128. C101 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265805 | 2 |
| #20265748 | 2 |
| #20265544 | 2 |
| #20265535 | 2 |
| #20265530 | 2 |
| #20265526 | 2 |
| #20265185 | 2 |
| #20265178 | 2 |
| C2×#15692180 | 2 |
| #20265132 | 2 |
| #416×C101 | 2 |
| #3137 | 101 |