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×#13108061 | C2 | semidirect |
| 2. C2×#15692263 | C2 | semidirect |
| 3. #20265751 | C2 | semidirect |
| 5. #20265426 | C2 | semidirect |
| 6. #20265409 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. #419×C101 | C2 | semidirect |
| 16. C2×#13108057 | C22 | semidirect |
| 18. C2×C8×D101 | C22 | semidirect |
| 24. #15692231 | C22 | semidirect |
| 28. #15692188 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 34. #103×C101 | C22 | semidirect |
| 50. C2×#11717579 | D4 | semidirect |
| 121. C101 | #3057 | semidirect |
| 129. #419 | D101 | semidirect |
| 154. #103 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108061 | 2 |
| C2×#15692263 | 2 |
| #20265751 | 2 |
| #20265746 | 2 |
| #20265426 | 2 |
| #20265409 | 2 |
| #20265213 | 2 |
| #20265183 | 2 |
| #419×C101 | 2 |
| #3057 | 101 |