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. #20266140 | C2 | semidirect |
| 4. C2×C8×#87938 | C2 | semidirect |
| 5. #20266052 | C2 | semidirect |
| 6. #20266049 | C2 | semidirect |
| 12. #15692320 | C4 | semidirect |
| 13. #15692319 | C4 | semidirect |
| 14. #15692318 | C4 | semidirect |
| 15. #15692317 | C4 | semidirect |
| 22. #15692263 | C4 | semidirect |
| 23. #15692262 | C4 | semidirect |
| 25. #15692261 | C4 | semidirect |
| 30. #131×C101 | C4 | semidirect |
| 128. C101 | #1764 | semidirect |
| 142. #131 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊#104 | 2 |
| #20266167 | 2 |
| #20266140 | 2 |
| C2×C8×#87938 | 2 |
| #20266052 | 2 |
| #20266049 | 2 |
| #131×D101 | 2 |
| #1764 | 101 |