Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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×#15692325 | C2 | semidirect |
| 3. #20266184 | C2 | semidirect |
| 5. #20266047 | C2 | semidirect |
| 6. (C2×#87938)⋊C8 | C2 | semidirect |
| 23. #15692180 | C4 | semidirect |
| 24. #15692178 | C4 | semidirect |
| 25. #15692176 | C4 | semidirect |
| 26. #102×C101 | C4 | semidirect |
| 110. C101 | #1866 | semidirect |
| 136. #102 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692342 | 2 |
| C2×#15692325 | 2 |
| #20266184 | 2 |
| C2×#15692319 | 2 |
| #20266047 | 2 |
| (C2×#87938)⋊C8 | 2 |
| #20265170 | 2 |
| #1866 | 101 |