Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13108059 | C2 | semidirect |
| 2. #20265741 | C2 | semidirect |
| 3. #20265652 | C2 | semidirect |
| 4. #20265394 | C2 | semidirect |
| 5. #20265370 | C2 | semidirect |
| 6. #20265205 | C2 | semidirect |
| 7. #20265183 | C2 | semidirect |
| 8. #20265173 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 14. #15692251 | C22 | semidirect |
| 15. #15692244 | C22 | semidirect |
| 19. D4×Dic101 | C22 | semidirect |
| 23. #15692184 | C22 | semidirect |
| 24. #15692179 | C22 | semidirect |
| 25. #15692177 | C22 | semidirect |
| 26. #15692176 | C22 | semidirect |
| 30. C2×SD16×C101 | C22 | semidirect |
| 31. C2×D8×C101 | C22 | semidirect |
| 58. C2×D4×C101 | D4 | semidirect |
| 122. C101 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D101 | semidirect |
| 136. C2×SD16 | C2×D101 | semidirect |
| 139. C2×D8 | C2×D101 | semidirect |
| 168. 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×#13108059 | 2 |
| #20265741 | 2 |
| #20265652 | 2 |
| #20265394 | 2 |
| #20265370 | 2 |
| #20265205 | 2 |
| #20265183 | 2 |
| #20265173 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3041 | 101 |