Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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×#15692302 | C2 | semidirect |
| 2. #20265992 | C2 | semidirect |
| 3. #20265988 | C2 | semidirect |
| 4. #20265975 | C2 | semidirect |
| 5. C2×#15692285 | C2 | semidirect |
| 6. #20265944 | C2 | semidirect |
| 7. #585×C101 | C2 | semidirect |
| 9. #15692302 | C22 | semidirect |
| 10. C2×#13108074 | C22 | semidirect |
| 12. C22×Dic202 | C22 | semidirect |
| 14. #15692286 | C22 | semidirect |
| 15. #15692285 | C22 | semidirect |
| 16. #15692285 | C22 | semidirect |
| 17. #15692281 | C22 | semidirect |
| 18. #15692280 | C22 | semidirect |
| 19. #15692275 | C22 | semidirect |
| 20. C2×#13108064 | C22 | semidirect |
| 21. C2×#13108062 | C22 | semidirect |
| 22. #15692262 | C22 | semidirect |
| 23. C2×#13108058 | C22 | semidirect |
| 25. 2−1+4×C101 | C22 | semidirect |
| 27. H(5,𝔽2)×C101 | C22 | semidirect |
| 113. C101 | #3586 | semidirect |
| 114. #585 | D101 | semidirect |
| 124. 2−1+4 | C2×D101 | semidirect |
| 126. H(5,𝔽2) | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| #20265992 | 2 |
| #20265988 | 2 |
| #20265975 | 2 |
| C2×#15692285 | 2 |
| #20265944 | 2 |
| #585×C101 | 2 |
| #3586 | 101 |