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×#15692288 | C2 | semidirect |
| 3. C2×#15692242 | C2 | semidirect |
| 4. #20265645 | C2 | semidirect |
| 5. #20265398 | C2 | semidirect |
| 6. #20265391 | C2 | semidirect |
| 7. #20265200 | C2 | semidirect |
| 8. #20265185 | C2 | semidirect |
| 9. #418×C101 | C2 | semidirect |
| 14. C2×Dic404 | C22 | semidirect |
| 15. C2×#13108063 | C22 | semidirect |
| 22. #15692220 | C22 | semidirect |
| 23. #15692217 | C22 | semidirect |
| 29. #15692184 | C22 | semidirect |
| 30. #15692178 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 135. #418 | 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×#15692281 | 2 |
| C2×#15692242 | 2 |
| #20265645 | 2 |
| #20265398 | 2 |
| #20265391 | 2 |
| #20265200 | 2 |
| #20265185 | 2 |
| #418×C101 | 2 |
| #3040 | 101 |