Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #20265991 | C2 | semidirect |
| 2. #20265988 | C2 | semidirect |
| 3. #20265560 | C2 | semidirect |
| 4. #20265452 | C2 | semidirect |
| 5. #20265444 | C2 | semidirect |
| 6. #20265438 | C2 | semidirect |
| 7. #20265355 | C2 | semidirect |
| 8. #20265348 | C2 | semidirect |
| 9. #20265294 | C2 | semidirect |
| 10. #20265292 | C2 | semidirect |
| 11. #576×C101 | C2 | semidirect |
| 12. #15692302 | C22 | semidirect |
| 15. #15692285 | C22 | semidirect |
| 18. #15692281 | C22 | semidirect |
| 22. C2×Dic404 | C22 | semidirect |
| 25. C2×#13108062 | C22 | semidirect |
| 26. #15692262 | C22 | semidirect |
| 27. #15692261 | C22 | semidirect |
| 28. #15692242 | C22 | semidirect |
| 29. #15692191 | C22 | semidirect |
| 30. #15692190 | C22 | semidirect |
| 32. #15692182 | C22 | semidirect |
| 33. #15692181 | C22 | semidirect |
| 34. #15692173 | C22 | semidirect |
| 35. #15692172 | C22 | semidirect |
| 36. C8×Dic101 | C22 | semidirect |
| 150. C101 | #3290 | semidirect |
| 153. #576 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265991 | 2 |
| #20265988 | 2 |
| #20265560 | 2 |
| #20265452 | 2 |
| #20265444 | 2 |
| #20265438 | 2 |
| #20265355 | 2 |
| #20265348 | 2 |
| #20265294 | 2 |
| #20265292 | 2 |
| #576×C101 | 2 |
| #3290 | 101 |