Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#15692286 | C2 | semidirect |
| 3. C2×#15692244 | C2 | semidirect |
| 4. #20265645 | C2 | semidirect |
| 5. #20265402 | C2 | semidirect |
| 6. #20265395 | C2 | semidirect |
| 7. #20265200 | C2 | semidirect |
| 8. #20265181 | C2 | semidirect |
| 9. #419×C101 | C2 | semidirect |
| 14. C2×#13108064 | C22 | semidirect |
| 16. C2×#13108061 | C22 | semidirect |
| 22. #15692220 | C22 | semidirect |
| 23. #15692217 | C22 | semidirect |
| 29. #15692184 | C22 | semidirect |
| 34. #103×C101 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 134. #419 | D101 | semidirect |
| 159. #103 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692286 | 2 |
| C2×#15692283 | 2 |
| C2×#15692244 | 2 |
| #20265645 | 2 |
| #20265402 | 2 |
| #20265395 | 2 |
| #20265200 | 2 |
| #20265181 | 2 |
| #419×C101 | 2 |
| #3040 | 101 |