Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C2×#15692263 | C2 | semidirect |
| 3. #20265298 | C2 | direct (N × H) |
| 4. C2×#15692181 | C2 | semidirect |
| 5. C2×#15692165 | C2 | semidirect |
| 6. C2×#108×C101 | C2 | semidirect |
| 8. #15692277 | C4 | semidirect |
| 10. C2×Dic404 | C4 | semidirect |
| 11. C2×#13108063 | C4 | semidirect |
| 12. C2×D808 | C4 | semidirect |
| 14. #15692263 | C22 | semidirect |
| 19. #15692181 | C22 | semidirect |
| 20. #15692165 | C22 | semidirect |
| 23. #108×C101 | C22 | semidirect |
| 33. Dic404 | C2×C4 | semidirect |
| 34. #13108063 | C2×C4 | semidirect |
| 35. D808 | C2×C4 | semidirect |
| 88. C2×C101 | #444 | semidirect |
| 92. C101 | C2×#444 | semidirect |
| 96. C2×#108 | D101 | semidirect |
| 113. #108 | C2×D101 | semidirect |
| 181. C2 | #20265298 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C2×#15692263 | 2 |
| #20265298 | 2 |
| C2×#15692181 | 2 |
| C2×#15692165 | 2 |
| C2×#108×C101 | 2 |
| C2×#444 | 101 |