Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13108062 | C2 | semidirect |
| 2. C2×#15692263 | C2 | semidirect |
| 3. #20265753 | C2 | semidirect |
| 5. #20265422 | C2 | semidirect |
| 6. #20265405 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265187 | C2 | semidirect |
| 9. #418×C101 | C2 | semidirect |
| 16. C2×#13108057 | C22 | semidirect |
| 18. C2×C8×D101 | C22 | semidirect |
| 24. #15692235 | C22 | semidirect |
| 28. #15692188 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 30. #15692180 | C22 | semidirect |
| 50. C2×#11717579 | D4 | semidirect |
| 121. C101 | #3057 | semidirect |
| 130. #418 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C2×#15692263 | 2 |
| #20265753 | 2 |
| #20265744 | 2 |
| #20265422 | 2 |
| #20265405 | 2 |
| #20265213 | 2 |
| #20265187 | 2 |
| #418×C101 | 2 |
| #3057 | 101 |