Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20265217 | C2 | semidirect |
| 3. C2×#15692183 | C2 | semidirect |
| 4. #20265176 | C2 | semidirect |
| 5. C2×#15692172 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 7. #390×C101 | C2 | semidirect |
| 40. #13108058 | D4 | semidirect |
| 131. C101 | #2037 | semidirect |
| 137. #390 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265744 | 2 |
| #20265217 | 2 |
| C2×#15692183 | 2 |
| #20265176 | 2 |
| C2×#15692172 | 2 |
| #20264937 | 2 |
| #390×C101 | 2 |
| #2037 | 101 |