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×#15692301 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265321 | C2 | semidirect |
| 5. #20265309 | C2 | semidirect |
| 6. #20265183 | C2 | semidirect |
| 7. #20265173 | C2 | semidirect |
| 8. #20265145 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 12. C2×#13108075 | C22 | semidirect |
| 18. C2×D4×D101 | C22 | semidirect |
| 20. C2×#13108059 | C22 | semidirect |
| 21. C22×#11717579 | C22 | semidirect |
| 24. #15692226 | C22 | semidirect |
| 26. #15692214 | C22 | semidirect |
| 27. #15692179 | C22 | semidirect |
| 28. #15692177 | C22 | semidirect |
| 29. #15692176 | C22 | semidirect |
| 30. #15692167 | C22 | semidirect |
| 32. C22×D4×C101 | C22 | semidirect |
| 34. C2×SD16×C101 | C22 | semidirect |
| 35. C2×D8×C101 | C22 | semidirect |
| 36. C2×M16×C101 | C22 | semidirect |
| 50. C2×D404 | D4 | semidirect |
| 69. #41×C101 | D4 | semidirect |
| 152. C101 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 172. C22×D4 | C2×D101 | semidirect |
| 174. C2×SD16 | C2×D101 | semidirect |
| 177. C2×D8 | C2×D101 | semidirect |
| 178. C2×M16 | C2×D101 | semidirect |
| 198. #41 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692301 | 2 |
| C22×#13108059 | 2 |
| #20265744 | 2 |
| #20265321 | 2 |
| #20265309 | 2 |
| #20265183 | 2 |
| #20265173 | 2 |
| #20265145 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3008 | 101 |