Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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×#13108063 | C2 | semidirect |
| 2. #20265748 | C2 | semidirect |
| 4. #20265423 | C2 | semidirect |
| 5. #20265406 | C2 | semidirect |
| 6. #20265215 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. C2×#131×C101 | C2 | semidirect |
| 20. #15692234 | C22 | semidirect |
| 25. #15692189 | C22 | semidirect |
| 26. #15692187 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 32. C2×M16×C101 | C22 | semidirect |
| 34. C22×C8×C101 | C22 | semidirect |
| 67. C2×C8×C101 | D4 | semidirect |
| 121. C101 | #3057 | semidirect |
| 123. C2×#131 | D101 | semidirect |
| 139. C2×M16 | C2×D101 | semidirect |
| 141. C22×C8 | C2×D101 | semidirect |
| 179. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108063 | 2 |
| #20265748 | 2 |
| #20265741 | 2 |
| #20265423 | 2 |
| #20265406 | 2 |
| #20265215 | 2 |
| #20265187 | 2 |
| #20265183 | 2 |
| C2×#131×C101 | 2 |
| #3057 | 101 |