Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #20265992 | C2 | semidirect |
| 2. #20265991 | C2 | semidirect |
| 3. #20265555 | C2 | semidirect |
| 4. #20265452 | C2 | semidirect |
| 5. #20265450 | C2 | semidirect |
| 6. #20265449 | C2 | semidirect |
| 7. #20265360 | C2 | semidirect |
| 8. #20265358 | C2 | semidirect |
| 9. #20265294 | C2 | semidirect |
| 10. #20265292 | C2 | semidirect |
| 11. #578×C101 | C2 | semidirect |
| 147. C101 | #3293 | semidirect |
| 150. #578 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265992 | 2 |
| #20265991 | 2 |
| #20265555 | 2 |
| #20265452 | 2 |
| #20265450 | 2 |
| #20265449 | 2 |
| #20265360 | 2 |
| #20265358 | 2 |
| #20265294 | 2 |
| #20265292 | 2 |
| #578×C101 | 2 |
| #3293 | 101 |