Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20266064 | C2 | semidirect |
| 4. C16×#87938 | C2 | semidirect |
| 8. #15692330 | C4 | semidirect |
| 9. #15692329 | C4 | semidirect |
| 16. #15692195 | C4 | semidirect |
| 17. #15692194 | C4 | semidirect |
| 19. M32×C101 | C4 | semidirect |
| 28. #13108077 | C2×C4 | semidirect |
| 35. #13108049 | C2×C4 | semidirect |
| 37. C16×C101 | C2×C4 | semidirect |
| 59. #87938 | M32 | direct (N × H) |
| 69. C101 | C4×M32 | semidirect |
| 82. M32 | #87938 | direct (N × H) |
| 106. C16 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊M32 | 2 |
| C2×C8×#87938 | 2 |
| #20266064 | 2 |
| C16×#87938 | 2 |
| M32×D101 | 2 |
| C4×M32 | 101 |