Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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. C23×#11717579 | C2 | semidirect |
| 3. C2×#15692229 | C2 | semidirect |
| 4. #20265411 | C2 | direct (N × H) |
| 5. C2×#15692188 | C2 | semidirect |
| 6. C2×#15692176 | C2 | semidirect |
| 7. C2×#15692175 | C2 | semidirect |
| 8. C2×#121×C101 | C2 | semidirect |
| 12. C2×#13108059 | C22 | semidirect |
| 16. C22×#11717579 | C22 | semidirect |
| 18. #15692229 | C22 | semidirect |
| 21. #15692188 | C22 | semidirect |
| 22. #15692176 | C22 | semidirect |
| 23. #15692175 | C22 | semidirect |
| 28. #121×C101 | C22 | semidirect |
| 42. C2×#11717579 | D4 | semidirect |
| 72. C23×C101 | D8 | semidirect |
| 101. #11717579 | C2×D4 | semidirect |
| 111. C22×C101 | C2×D8 | semidirect |
| 126. C2×C101 | #466 | semidirect |
| 132. C101 | C2×#466 | semidirect |
| 136. C2×#121 | D101 | semidirect |
| 155. #121 | C2×D101 | semidirect |
| 208. C23 | #13108059 | semidirect |
| 247. C22 | C2×#13108059 | semidirect |
| 259. C2 | #20265411 | 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 |
| C23×#11717579 | 2 |
| C2×#15692229 | 2 |
| #20265411 | 2 |
| C2×#15692188 | 2 |
| C2×#15692176 | 2 |
| C2×#15692175 | 2 |
| C2×#121×C101 | 2 |
| C2×#466 | 101 |