Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
406 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20266227 | C2 | semidirect |
| 2. #20266206 | C2 | semidirect |
| 3. D4×#11717581 | C2 | semidirect |
| 4. #20266199 | C2 | semidirect |
| 5. #20266198 | C2 | semidirect |
| 6. C4×#13108084 | C2 | semidirect |
| 7. C2×#15692310 | C2 | semidirect |
| 62. D4×C101 | M16 | semidirect |
| 82. #11717581 | #41 | semidirect |
| 105. C101 | #2970 | semidirect |
| 169. D4 | #13108084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266227 | 2 |
| #20266206 | 2 |
| D4×#11717581 | 2 |
| #20266199 | 2 |
| #20266198 | 2 |
| C4×#13108084 | 2 |
| C2×#15692310 | 2 |
| C4×#13108073 | 2 |
| #2970 | 101 |