Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
616 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×C8×D101 | C2 | semidirect |
| 3. C2×#15692230 | C2 | semidirect |
| 4. C2×#15692226 | C2 | semidirect |
| 5. #20265412 | C2 | direct (N × H) |
| 6. C2×#15692188 | C2 | semidirect |
| 7. C2×#15692177 | C2 | semidirect |
| 8. C2×#102×C101 | C2 | semidirect |
| 14. C2×#13108059 | C22 | semidirect |
| 17. C2×C8×D101 | C22 | semidirect |
| 19. #15692230 | C22 | semidirect |
| 21. #15692226 | C22 | semidirect |
| 25. #15692188 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 30. #102×C101 | C22 | semidirect |
| 48. C2×#11717579 | D4 | semidirect |
| 77. C22×D101 | D8 | semidirect |
| 101. #11717579 | C2×D4 | semidirect |
| 117. C2×D101 | C2×D8 | semidirect |
| 125. C2×C101 | #466 | semidirect |
| 132. C101 | C2×#466 | semidirect |
| 140. C2×#102 | D101 | semidirect |
| 162. #102 | C2×D101 | semidirect |
| 259. C2 | #20265412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108059 | 2 |
| C22×C8×D101 | 2 |
| C2×#15692230 | 2 |
| C2×#15692226 | 2 |
| #20265412 | 2 |
| C2×#15692188 | 2 |
| C2×#15692177 | 2 |
| C2×#102×C101 | 2 |
| C2×#466 | 101 |