Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
656 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 322 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. C4×#13108084 | C2 | direct (N × H) |
| 3. C2×#15692310 | C2 | semidirect |
| 4. C2×C4×#11717581 | C2 | semidirect |
| 6. C2×#13108084 | C4 | direct (N × H) |
| 9. #15692310 | C22 | semidirect |
| 10. C4×#11717581 | C22 | semidirect |
| 20. #13108084 | C2×C4 | direct (N × H) |
| 21. C2×#11717581 | C2×C4 | semidirect |
| 50. C2×C4×C101 | M16 | semidirect |
| 55. C2×Dic101 | M16 | semidirect |
| 65. #11717581 | C22×C4 | semidirect |
| 76. C4×C101 | C2×M16 | semidirect |
| 79. Dic101 | C2×M16 | semidirect |
| 81. C2×C101 | C4×M16 | semidirect |
| 87. C101 | C2×C4×M16 | semidirect |
| 148. C2×C4 | #13108084 | direct (N × H) |
| 167. C4 | C2×#13108084 | direct (N × H) |
| 169. C2 | C4×#13108084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108084 | 2 |
| C4×#13108084 | 2 |
| C2×#15692310 | 2 |
| C2×C4×#11717581 | 2 |
| C2×C42×D101 | 2 |
| C2×C4×M16 | 101 |