Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692286 | C2 | semidirect |
| 3. #20265943 | C2 | semidirect |
| 4. #20265449 | C2 | semidirect |
| 5. #20265437 | C2 | semidirect |
| 6. #20265226 | C2 | semidirect |
| 7. #20265161 | C2 | semidirect |
| 8. C2×#15692174 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 26. #15692191 | C22 | semidirect |
| 27. #15692174 | C22 | semidirect |
| 28. #15692174 | C22 | semidirect |
| 29. #15692172 | C22 | semidirect |
| 34. C2×Q16×C101 | C22 | semidirect |
| 35. C2×SD16×C101 | C22 | semidirect |
| 143. C101 | #3069 | semidirect |
| 146. C2×#137 | D101 | semidirect |
| 166. C2×Q16 | C2×D101 | semidirect |
| 168. C2×SD16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265975 | 2 |
| C2×#15692286 | 2 |
| #20265943 | 2 |
| #20265449 | 2 |
| #20265437 | 2 |
| #20265226 | 2 |
| #20265161 | 2 |
| C2×#15692174 | 2 |
| C2×#137×C101 | 2 |
| #3069 | 101 |