Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#15692286 | C2 | semidirect |
| 3. C4×#13108074 | C2 | semidirect |
| 4. #20265396 | C2 | semidirect |
| 5. #20265389 | C2 | semidirect |
| 6. #20265201 | C2 | semidirect |
| 7. #20265186 | C2 | semidirect |
| 8. #20265182 | C2 | semidirect |
| 9. C2×#124×C101 | C2 | semidirect |
| 13. C2×#13108064 | C22 | semidirect |
| 15. C2×#13108061 | C22 | semidirect |
| 19. C4×Dic202 | C22 | semidirect |
| 20. C4×D404 | C22 | semidirect |
| 25. C4⋊#11717579 | C22 | semidirect |
| 26. #15692179 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 129. C2×#124 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692286 | 2 |
| C2×#15692281 | 2 |
| C4×#13108074 | 2 |
| #20265396 | 2 |
| #20265389 | 2 |
| #20265201 | 2 |
| #20265186 | 2 |
| #20265182 | 2 |
| C2×#124×C101 | 2 |
| #3040 | 101 |