Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20266142 | C2 | semidirect |
| 4. C2×C8×#87938 | C2 | semidirect |
| 5. #20266053 | C2 | semidirect |
| 6. #20266047 | C2 | semidirect |
| 9. #15692343 | C4 | semidirect |
| 16. #15692320 | C4 | semidirect |
| 23. #15692179 | C4 | semidirect |
| 24. #15692177 | C4 | semidirect |
| 25. #15692175 | C4 | semidirect |
| 26. #103×C101 | C4 | semidirect |
| 110. C101 | #1764 | semidirect |
| 131. #103 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692343 | 2 |
| C2×#15692320 | 2 |
| #20266142 | 2 |
| C2×C8×#87938 | 2 |
| #20266053 | 2 |
| #20266047 | 2 |
| #20265172 | 2 |
| #1764 | 101 |