Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#15692281 | C2 | semidirect |
| 2. C2×#15692277 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265658 | C2 | semidirect |
| 5. #20265398 | C2 | semidirect |
| 6. #20265391 | C2 | semidirect |
| 7. #20265376 | C2 | semidirect |
| 8. #20265371 | C2 | semidirect |
| 9. #20265203 | C2 | semidirect |
| 10. #20265176 | C2 | semidirect |
| 11. C2×#102×C101 | C2 | semidirect |
| 16. C2×Dic404 | C22 | semidirect |
| 17. C2×#13108063 | C22 | semidirect |
| 18. C2×#13108063 | C22 | semidirect |
| 20. C2×D808 | C22 | semidirect |
| 28. #15692220 | C22 | semidirect |
| 29. #15692217 | C22 | semidirect |
| 34. #15692184 | C22 | semidirect |
| 35. #15692184 | C22 | semidirect |
| 36. #15692178 | C22 | semidirect |
| 37. #15692175 | C22 | semidirect |
| 46. #13108074 | D4 | semidirect |
| 155. C101 | #3045 | semidirect |
| 166. C2×#102 | 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×#15692277 | 2 |
| #20265744 | 2 |
| #20265658 | 2 |
| #20265398 | 2 |
| #20265391 | 2 |
| #20265376 | 2 |
| #20265371 | 2 |
| #20265203 | 2 |
| #20265176 | 2 |
| C2×#102×C101 | 2 |
| #3045 | 101 |