Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13108061 | C2 | semidirect |
| 2. C22×#13108057 | C2 | semidirect |
| 3. C2×#15692231 | C2 | semidirect |
| 5. #20265426 | C2 | direct (N × H) |
| 6. C2×#15692188 | C2 | semidirect |
| 7. C2×#15692177 | C2 | semidirect |
| 8. C2×#103×C101 | C2 | semidirect |
| 13. C2×#13108061 | C22 | semidirect |
| 15. C2×#13108057 | C22 | semidirect |
| 18. #15692231 | C22 | semidirect |
| 25. #15692188 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 30. #103×C101 | C22 | semidirect |
| 47. C2×#11717579 | D4 | semidirect |
| 97. #11717579 | C2×D4 | semidirect |
| 117. C2×C101 | #468 | semidirect |
| 124. C101 | C2×#468 | semidirect |
| 131. C2×#103 | D101 | semidirect |
| 153. #103 | C2×D101 | semidirect |
| 243. C2 | #20265426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108061 | 2 |
| C22×#13108057 | 2 |
| C2×#15692231 | 2 |
| C2×#15692230 | 2 |
| #20265426 | 2 |
| C2×#15692188 | 2 |
| C2×#15692177 | 2 |
| C2×#103×C101 | 2 |
| C2×#468 | 101 |