Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15692285 | C2 | semidirect |
| 2. C22×#13108062 | C2 | semidirect |
| 3. #20265748 | C2 | semidirect |
| 4. #20265339 | C2 | semidirect |
| 5. #20265328 | C2 | semidirect |
| 6. #20265182 | C2 | semidirect |
| 7. #20265173 | C2 | semidirect |
| 8. #20265144 | C2 | semidirect |
| 10. C22×Dic202 | C22 | semidirect |
| 12. C2×#13108064 | C22 | semidirect |
| 14. C2×#13108062 | C22 | semidirect |
| 15. C2×#13108062 | C22 | semidirect |
| 16. C2×#13108058 | C22 | semidirect |
| 17. C22×#11717579 | C22 | semidirect |
| 21. #15692234 | C22 | semidirect |
| 22. #15692214 | C22 | semidirect |
| 23. #15692179 | C22 | semidirect |
| 24. #15692176 | C22 | semidirect |
| 25. #15692176 | C22 | semidirect |
| 26. C22⋊#11717579 | C22 | semidirect |
| 147. C101 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| C22×#13108062 | 2 |
| #20265748 | 2 |
| #20265339 | 2 |
| #20265328 | 2 |
| #20265182 | 2 |
| #20265173 | 2 |
| #20265144 | 2 |
| C2×H(5,𝔽2)×C101 | 2 |
| #3009 | 101 |