Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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×#15692300 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. C22×#13108059 | C2 | semidirect |
| 4. #20265746 | C2 | semidirect |
| 5. #20265323 | C2 | semidirect |
| 6. #20265312 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #20265145 | C2 | semidirect |
| 9. #418×C101 | C2 | semidirect |
| 15. C2×#13108073 | C22 | semidirect |
| 16. C22×D404 | C22 | semidirect |
| 19. C2×D4×D101 | C22 | semidirect |
| 21. C2×#13108063 | C22 | semidirect |
| 22. C2×D808 | C22 | semidirect |
| 24. C2×#13108059 | C22 | semidirect |
| 25. C22×#11717579 | C22 | semidirect |
| 28. #15692230 | C22 | semidirect |
| 30. #15692178 | C22 | semidirect |
| 31. #15692175 | C22 | semidirect |
| 32. #15692167 | C22 | semidirect |
| 34. C2×M16×C101 | C22 | semidirect |
| 35. #117×C101 | C22 | semidirect |
| 36. #102×C101 | C22 | semidirect |
| 42. #13108074 | D4 | semidirect |
| 75. C2×D4×C101 | D4 | semidirect |
| 152. C101 | #3008 | semidirect |
| 159. #418 | D101 | semidirect |
| 178. C2×M16 | C2×D101 | semidirect |
| 184. #117 | C2×D101 | semidirect |
| 187. #102 | C2×D101 | semidirect |
| 218. C2×D4 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692300 | 2 |
| C2×#15692283 | 2 |
| C22×#13108059 | 2 |
| #20265746 | 2 |
| #20265323 | 2 |
| #20265312 | 2 |
| #20265171 | 2 |
| #20265145 | 2 |
| #418×C101 | 2 |
| #3008 | 101 |