Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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. C2×#15692274 | C2 | semidirect |
| 2. C22×Dic404 | C2 | semidirect |
| 3. #20265833 | C2 | semidirect |
| 4. #20265560 | C2 | semidirect |
| 5. #20265419 | C2 | semidirect |
| 6. #20265398 | C2 | semidirect |
| 7. #20265340 | C2 | semidirect |
| 8. #20265315 | C2 | semidirect |
| 9. #20265271 | C2 | semidirect |
| 10. C8×C22⋊D101 | C2 | semidirect |
| 11. #466×C101 | C2 | semidirect |
| 55. Dic404 | D4 | semidirect |
| 116. C22×C101 | #135 | semidirect |
| 137. C101 | #3285 | semidirect |
| 143. #466 | D101 | semidirect |
| 256. C22 | #15692274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692274 | 2 |
| C22×Dic404 | 2 |
| #20265833 | 2 |
| #20265560 | 2 |
| #20265419 | 2 |
| #20265398 | 2 |
| #20265340 | 2 |
| #20265315 | 2 |
| #20265271 | 2 |
| C8×C22⋊D101 | 2 |
| #466×C101 | 2 |
| #3285 | 101 |