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×#15692286 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. C2×#15692277 | C2 | semidirect |
| 4. #20265751 | C2 | semidirect |
| 5. #20265744 | C2 | semidirect |
| 6. #20265568 | C2 | semidirect |
| 7. #20265563 | C2 | semidirect |
| 8. #20265558 | C2 | semidirect |
| 9. #20265548 | C2 | semidirect |
| 10. #20265132 | C2 | semidirect |
| 11. C22×SD16×C101 | C2 | semidirect |
| 17. C2×Dic404 | C22 | semidirect |
| 18. C2×#13108064 | C22 | semidirect |
| 19. C2×#13108063 | C22 | semidirect |
| 20. C2×#13108063 | C22 | semidirect |
| 22. C2×#13108061 | C22 | semidirect |
| 23. C2×D808 | C22 | semidirect |
| 26. #15692253 | C22 | semidirect |
| 28. #15692244 | C22 | semidirect |
| 35. #15692165 | C22 | semidirect |
| 36. C8×Dic101 | C22 | semidirect |
| 64. #13108058 | D4 | semidirect |
| 85. C2×C8×C101 | D4 | semidirect |
| 149. C101 | #3154 | semidirect |
| 153. C22×SD16 | D101 | semidirect |
| 228. C2×C8 | C22⋊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 |
| C2×#15692277 | 2 |
| #20265751 | 2 |
| #20265744 | 2 |
| #20265568 | 2 |
| #20265563 | 2 |
| #20265558 | 2 |
| #20265548 | 2 |
| #20265132 | 2 |
| C22×SD16×C101 | 2 |
| #3154 | 101 |