Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265732 | C2 | semidirect |
| 3. #20265540 | C2 | semidirect |
| 4. #20265525 | C2 | semidirect |
| 5. #20265524 | C2 | semidirect |
| 6. #20265523 | C2 | semidirect |
| 7. #20265180 | C2 | semidirect |
| 8. C4×#13108057 | C2 | semidirect |
| 9. #486×C101 | C2 | semidirect |
| 14. #15692255 | C22 | semidirect |
| 19. #15692246 | C22 | semidirect |
| 26. #15692177 | C22 | semidirect |
| 27. #15692176 | C22 | semidirect |
| 28. #15692175 | C22 | semidirect |
| 29. #15692165 | C22 | semidirect |
| 30. C4×#11717579 | C22 | semidirect |
| 31. C4⋊Q8×C101 | C22 | semidirect |
| 33. #102×C101 | C22 | semidirect |
| 34. C4×C8×C101 | C22 | semidirect |
| 124. C101 | #3138 | semidirect |
| 131. #486 | D101 | semidirect |
| 139. C4⋊Q8 | C2×D101 | semidirect |
| 155. #102 | C2×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 |
|---|---|
| #20265732 | 2 |
| #127×D101 | 2 |
| #20265540 | 2 |
| #20265525 | 2 |
| #20265524 | 2 |
| #20265523 | 2 |
| #20265180 | 2 |
| C4×#13108057 | 2 |
| #486×C101 | 2 |
| #3138 | 101 |