Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#13108059 | C2 | semidirect |
| 2. C2×#15692262 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265428 | C2 | semidirect |
| 5. #20265411 | C2 | semidirect |
| 6. #20265213 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. #535×C101 | C2 | semidirect |
| 16. C2×#13108058 | C22 | semidirect |
| 18. C22×#11717579 | C22 | semidirect |
| 21. #15692229 | C22 | semidirect |
| 24. #15692188 | C22 | semidirect |
| 25. #15692186 | C22 | semidirect |
| 26. #15692176 | C22 | semidirect |
| 27. #15692175 | C22 | semidirect |
| 32. #121×C101 | C22 | semidirect |
| 46. C2×#11717579 | D4 | semidirect |
| 126. C101 | #3058 | semidirect |
| 130. #535 | D101 | semidirect |
| 152. #121 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108059 | 2 |
| C2×#15692262 | 2 |
| #20265741 | 2 |
| #20265428 | 2 |
| #20265411 | 2 |
| #20265213 | 2 |
| #20265182 | 2 |
| #20265181 | 2 |
| #535×C101 | 2 |
| #3058 | 101 |