Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692288 | C2 | semidirect |
| 2. C2×#15692275 | C2 | semidirect |
| 3. C22×#13108062 | C2 | semidirect |
| 4. #20265748 | C2 | semidirect |
| 5. #20265744 | C2 | semidirect |
| 6. #20265568 | C2 | semidirect |
| 7. #20265565 | C2 | semidirect |
| 8. #20265560 | C2 | semidirect |
| 9. #20265548 | C2 | semidirect |
| 10. #20265135 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 16. C2×Dic404 | C22 | semidirect |
| 17. C2×#13108064 | C22 | semidirect |
| 18. C2×#13108063 | C22 | semidirect |
| 22. C2×#13108062 | C22 | semidirect |
| 23. C2×#13108061 | C22 | semidirect |
| 24. C2×#13108059 | C22 | semidirect |
| 26. #15692253 | C22 | semidirect |
| 29. #15692242 | C22 | semidirect |
| 35. #15692165 | C22 | semidirect |
| 36. C8×Dic101 | C22 | semidirect |
| 63. C2×#11717579 | D4 | semidirect |
| 86. M16×C101 | D4 | semidirect |
| 149. C101 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 226. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| C2×#15692275 | 2 |
| C22×#13108062 | 2 |
| #20265748 | 2 |
| #20265744 | 2 |
| #20265568 | 2 |
| #20265565 | 2 |
| #20265560 | 2 |
| #20265548 | 2 |
| #20265135 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3154 | 101 |