Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #20265897 | C2 | semidirect |
| 2. #20265580 | C2 | semidirect |
| 3. #20265512 | C2 | semidirect |
| 4. #20265498 | C2 | semidirect |
| 5. #20265459 | C2 | semidirect |
| 6. #20265457 | C2 | semidirect |
| 7. #20265421 | C2 | semidirect |
| 8. C4×#13108062 | C2 | semidirect |
| 9. #20265255 | C2 | semidirect |
| 10. #20265217 | C2 | semidirect |
| 99. #11717579 | #41 | semidirect |
| 123. C101 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265897 | 2 |
| #20265580 | 2 |
| #20265512 | 2 |
| #20265498 | 2 |
| #20265459 | 2 |
| #20265457 | 2 |
| #20265421 | 2 |
| C4×#13108062 | 2 |
| #20265255 | 2 |
| #20265217 | 2 |
| #547×C101 | 2 |
| #3353 | 101 |