Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20266068 | C2 | semidirect |
| 4. #20266067 | C2 | semidirect |
| 9. #15692329 | C4 | semidirect |
| 10. D101⋊C16 | C4 | semidirect |
| 16. #15692195 | C4 | semidirect |
| 18. C16×D101 | C4 | semidirect |
| 19. M32×C101 | C4 | semidirect |
| 28. #13108077 | C2×C4 | semidirect |
| 35. #13108049 | C2×C4 | semidirect |
| 37. C16×C101 | C2×C4 | semidirect |
| 67. D101 | #347 | semidirect |
| 69. C101 | C2×#347 | semidirect |
| 82. M32 | #87938 | semidirect |
| 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×#15692309 | 2 |
| #20266068 | 2 |
| #20266067 | 2 |
| M32×D101 | 2 |
| C2×#347 | 101 |