Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#15692281 | C2 | semidirect |
| 2. C2×#15692275 | C2 | semidirect |
| 3. #20265657 | C2 | semidirect |
| 4. #20265396 | C2 | semidirect |
| 5. #20265389 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265369 | C2 | semidirect |
| 8. #20265204 | C2 | semidirect |
| 9. #20265178 | C2 | semidirect |
| 10. C2×#15692176 | C2 | semidirect |
| 11. #535×C101 | C2 | semidirect |
| 15. C2×#13108064 | C22 | semidirect |
| 17. C2×#13108062 | C22 | semidirect |
| 18. C2×#13108061 | C22 | semidirect |
| 20. C2×#13108059 | C22 | semidirect |
| 23. C4×Dic202 | C22 | semidirect |
| 24. C4×D404 | C22 | semidirect |
| 29. C4⋊#11717579 | C22 | semidirect |
| 30. C4⋊#11717579 | C22 | semidirect |
| 31. #15692179 | C22 | semidirect |
| 34. #15692176 | C22 | semidirect |
| 44. #13108074 | D4 | semidirect |
| 155. C101 | #3045 | semidirect |
| 158. #535 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| C2×#15692275 | 2 |
| #20265657 | 2 |
| #20265396 | 2 |
| #20265389 | 2 |
| #20265374 | 2 |
| #20265369 | 2 |
| #20265204 | 2 |
| #20265178 | 2 |
| C2×#15692176 | 2 |
| #535×C101 | 2 |
| #3045 | 101 |