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×#15692283 | C2 | semidirect |
| 2. C2×#15692277 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265657 | C2 | semidirect |
| 5. #20265400 | C2 | semidirect |
| 6. #20265393 | C2 | semidirect |
| 7. #20265378 | C2 | semidirect |
| 8. #20265373 | C2 | semidirect |
| 9. #20265179 | C2 | semidirect |
| 10. C2×#15692177 | C2 | semidirect |
| 11. #424×C101 | C2 | semidirect |
| 17. C2×Dic404 | C22 | semidirect |
| 19. C2×#13108063 | C22 | semidirect |
| 20. C2×#13108063 | C22 | semidirect |
| 22. C2×D808 | C22 | semidirect |
| 28. C4×Dic202 | C22 | semidirect |
| 29. C4×D404 | C22 | semidirect |
| 34. #15692180 | C22 | semidirect |
| 37. #15692177 | C22 | semidirect |
| 41. C4⋊C8×C101 | C22 | semidirect |
| 42. C4⋊C8×C101 | C22 | semidirect |
| 47. #13108074 | D4 | semidirect |
| 155. C101 | #3045 | semidirect |
| 164. #424 | D101 | semidirect |
| 192. C4⋊C8 | C2×D101 | semidirect |
| 193. 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×#15692283 | 2 |
| C2×#15692277 | 2 |
| #20265746 | 2 |
| #20265657 | 2 |
| #20265400 | 2 |
| #20265393 | 2 |
| #20265378 | 2 |
| #20265373 | 2 |
| #20265179 | 2 |
| C2×#15692177 | 2 |
| #424×C101 | 2 |
| #3045 | 101 |