Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265529 | C2 | semidirect |
| 3. #20265518 | C2 | semidirect |
| 4. #20265454 | C2 | semidirect |
| 5. #20265416 | C2 | semidirect |
| 6. #20265387 | C2 | semidirect |
| 7. #20265337 | C2 | semidirect |
| 8. C4×#13108061 | C2 | semidirect |
| 9. D4×#11717579 | C2 | semidirect |
| 10. #20265171 | C2 | semidirect |
| 11. #556×C101 | C2 | semidirect |
| 126. C101 | #3302 | semidirect |
| 127. #556 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265832 | 2 |
| #20265529 | 2 |
| #20265518 | 2 |
| #20265454 | 2 |
| #20265416 | 2 |
| #20265387 | 2 |
| #20265337 | 2 |
| C4×#13108061 | 2 |
| D4×#11717579 | 2 |
| #20265171 | 2 |
| #556×C101 | 2 |
| #3302 | 101 |