Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692281 | C2 | semidirect |
| 2. #20265744 | C2 | semidirect |
| 3. #20265652 | C2 | semidirect |
| 4. #20265390 | C2 | semidirect |
| 5. #20265370 | C2 | semidirect |
| 6. #20265203 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265174 | C2 | semidirect |
| 9. C22×D8×C101 | C2 | semidirect |
| 12. C2×#13108062 | C22 | semidirect |
| 13. C2×#13108059 | C22 | semidirect |
| 15. #15692251 | C22 | semidirect |
| 16. #15692242 | C22 | semidirect |
| 20. D4×Dic101 | C22 | semidirect |
| 24. #15692184 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 27. #15692176 | C22 | semidirect |
| 60. C2×D4×C101 | D4 | semidirect |
| 122. C101 | #3041 | semidirect |
| 124. C22×D8 | D101 | semidirect |
| 168. C2×D4 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| #20265744 | 2 |
| #20265652 | 2 |
| #20265390 | 2 |
| #20265370 | 2 |
| #20265203 | 2 |
| #20265182 | 2 |
| #20265174 | 2 |
| C22×D8×C101 | 2 |
| #3041 | 101 |