Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #20265808 | C2 | semidirect |
| 3. #20265540 | C2 | semidirect |
| 4. #20265535 | C2 | semidirect |
| 5. #20265530 | C2 | semidirect |
| 6. #20265522 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265176 | C2 | semidirect |
| 9. #20265174 | C2 | semidirect |
| 10. #20265132 | C2 | semidirect |
| 11. C2×#102×C101 | C2 | semidirect |
| 15. #15692254 | C22 | semidirect |
| 18. #15692246 | C22 | semidirect |
| 26. #15692180 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 28. #15692178 | C22 | semidirect |
| 29. #15692177 | C22 | semidirect |
| 30. #15692177 | C22 | semidirect |
| 33. #15692175 | C22 | semidirect |
| 34. #15692165 | C22 | semidirect |
| 35. C8×Dic101 | C22 | semidirect |
| 136. C101 | #3136 | semidirect |
| 146. C2×#102 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265808 | 2 |
| #20265744 | 2 |
| #20265540 | 2 |
| #20265535 | 2 |
| #20265530 | 2 |
| #20265522 | 2 |
| #20265182 | 2 |
| #20265176 | 2 |
| #20265174 | 2 |
| #20265132 | 2 |
| C2×#102×C101 | 2 |
| #3136 | 101 |