Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×#15692198 | C2 | semidirect |
| 3. #20265415 | C2 | semidirect |
| 4. #20264981 | C2 | semidirect |
| 5. #20264979 | C2 | semidirect |
| 6. #20264956 | C2 | semidirect |
| 7. C2×Q32×C101 | C2 | semidirect |
| 86. C101 | #2189 | semidirect |
| 88. C2×Q32 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×#15692198 | 2 |
| #20265415 | 2 |
| #20264981 | 2 |
| #20264979 | 2 |
| #20264956 | 2 |
| C2×Q32×C101 | 2 |
| #2189 | 101 |