Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20265730 | C2 | semidirect |
| 5. #20264949 | C2 | semidirect |
| 6. #20264936 | C2 | semidirect |
| 7. H(3,ℤ/4)×C101 | C2 | semidirect |
| 28. C2×Dic202 | Q8 | semidirect |
| 29. C2×D404 | Q8 | semidirect |
| 103. C101 | #2031 | semidirect |
| 110. H(3,ℤ/4) | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265730 | 2 |
| #20265195 | 2 |
| C2×#15692181 | 2 |
| #20265150 | 2 |
| #20264949 | 2 |
| #20264936 | 2 |
| H(3,ℤ/4)×C101 | 2 |
| #2031 | 101 |