Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #20265805 | C2 | semidirect |
| 3. #20265479 | C2 | semidirect |
| 4. #20265475 | C2 | semidirect |
| 5. #20265465 | C2 | semidirect |
| 6. #20265455 | C2 | semidirect |
| 7. #20265219 | C2 | semidirect |
| 8. #20265213 | C2 | semidirect |
| 9. #20265205 | C2 | semidirect |
| 14. #15692254 | C22 | semidirect |
| 16. #15692246 | C22 | semidirect |
| 26. #15692189 | C22 | semidirect |
| 27. #15692188 | C22 | semidirect |
| 28. #15692188 | C22 | semidirect |
| 29. #15692187 | C22 | semidirect |
| 30. #15692186 | C22 | semidirect |
| 31. #15692186 | C22 | semidirect |
| 32. #15692184 | C22 | semidirect |
| 33. #15692184 | C22 | semidirect |
| 66. C2×D4×C101 | Q8 | semidirect |
| 125. C101 | #3081 | semidirect |
| 170. C2×D4 | Dic202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265805 | 2 |
| #20265652 | 2 |
| #20265479 | 2 |
| #20265475 | 2 |
| #20265465 | 2 |
| #20265455 | 2 |
| #20265219 | 2 |
| #20265213 | 2 |
| #20265205 | 2 |
| C2×#15692176 | 2 |
| #418×C101 | 2 |
| #3081 | 101 |