Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#13108073 | C2 | semidirect |
| 2. C2×#15692285 | C2 | semidirect |
| 3. #20265684 | C2 | semidirect |
| 4. #20265336 | C2 | semidirect |
| 5. #20265319 | C2 | semidirect |
| 6. #20265187 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265140 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 19. C2×#13108064 | C22 | semidirect |
| 20. C2×#13108062 | C22 | semidirect |
| 23. #15692231 | C22 | semidirect |
| 24. #15692226 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 29. #15692176 | C22 | semidirect |
| 30. #15692167 | C22 | semidirect |
| 34. C2×SD16×C101 | C22 | semidirect |
| 35. C2×D8×C101 | C22 | semidirect |
| 43. C2×Dic202 | D4 | semidirect |
| 73. C2×D4×C101 | D4 | semidirect |
| 146. C101 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 170. C2×SD16 | C2×D101 | semidirect |
| 171. C2×D8 | C2×D101 | semidirect |
| 201. C2×D4 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C2×#15692285 | 2 |
| #20265684 | 2 |
| #20265336 | 2 |
| #20265319 | 2 |
| #20265187 | 2 |
| #20265182 | 2 |
| #20265140 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3005 | 101 |