Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692288 | C2 | semidirect |
| 3. C2×#15692243 | C2 | semidirect |
| 4. C4×#13108074 | C2 | semidirect |
| 5. #20265400 | C2 | semidirect |
| 6. #20265393 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. #423×C101 | C2 | semidirect |
| 15. C2×Dic404 | C22 | semidirect |
| 17. C2×#13108063 | C22 | semidirect |
| 22. C4×Dic202 | C22 | semidirect |
| 23. C4×D404 | C22 | semidirect |
| 29. #15692180 | C22 | semidirect |
| 34. C4⋊C8×C101 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 133. #423 | D101 | semidirect |
| 158. C4⋊C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| C2×#15692283 | 2 |
| C2×#15692243 | 2 |
| C4×#13108074 | 2 |
| #20265400 | 2 |
| #20265393 | 2 |
| #20265187 | 2 |
| #20265183 | 2 |
| #423×C101 | 2 |
| #3040 | 101 |