Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #20265218 | C2 | semidirect |
| 4. #20265216 | C2 | semidirect |
| 5. #20265215 | C2 | semidirect |
| 6. #20265213 | C2 | semidirect |
| 7. #427×C101 | C2 | semidirect |
| 9. C2×#13108057 | C4 | semidirect |
| 20. #15692189 | C22 | semidirect |
| 21. #15692188 | C22 | semidirect |
| 22. #15692187 | C22 | semidirect |
| 23. #15692186 | C22 | semidirect |
| 26. #107×C101 | C22 | semidirect |
| 27. #106×C101 | C22 | semidirect |
| 35. #13108057 | C2×C4 | semidirect |
| 36. #13108057 | C2×C4 | semidirect |
| 37. C2×#11717579 | C2×C4 | semidirect |
| 46. C2×C8×C101 | C2×C4 | semidirect |
| 88. C101 | #2911 | semidirect |
| 95. #427 | D101 | semidirect |
| 112. #107 | C2×D101 | semidirect |
| 115. #106 | C2×D101 | semidirect |
| 128. C2×C8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108057 | 2 |
| #117×D101 | 2 |
| #20265218 | 2 |
| #20265216 | 2 |
| #20265215 | 2 |
| #20265213 | 2 |
| #427×C101 | 2 |
| #2911 | 101 |