Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×C4×D404 | C2 | semidirect |
| 2. #20265488 | C2 | semidirect |
| 3. #20265454 | C2 | semidirect |
| 4. #20265369 | C2 | semidirect |
| 5. #20265310 | C2 | semidirect |
| 6. C4×#13108059 | C2 | semidirect |
| 7. #20265230 | C2 | semidirect |
| 8. #532×C101 | C2 | semidirect |
| 18. #15692188 | C22 | semidirect |
| 19. C4⋊#11717579 | C22 | semidirect |
| 20. #15692176 | C22 | semidirect |
| 23. C4×#11717579 | C22 | semidirect |
| 25. C4⋊Q8×C101 | C22 | semidirect |
| 26. #127×C101 | C22 | semidirect |
| 31. C4×D4×C101 | C22 | semidirect |
| 80. C2×C4×C101 | D8 | semidirect |
| 91. D404 | #41 | semidirect |
| 121. C101 | #3100 | semidirect |
| 122. #532 | D101 | semidirect |
| 134. C4⋊Q8 | C2×D101 | semidirect |
| 135. #127 | C2×D101 | semidirect |
| 144. C4×D4 | C2×D101 | semidirect |
| 208. C2×C4 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D404 | 2 |
| #20265488 | 2 |
| #20265454 | 2 |
| #20265369 | 2 |
| #20265310 | 2 |
| C4×#13108059 | 2 |
| #20265230 | 2 |
| #532×C101 | 2 |
| #3100 | 101 |