Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×Dic202 | C2 | semidirect |
| 3. C4×#13108062 | C2 | direct (N × H) |
| 4. C2×#15692186 | C2 | semidirect |
| 5. C2×#15692178 | C2 | semidirect |
| 7. C2×C4×#11717579 | C2 | semidirect |
| 10. C2×#13108062 | C4 | direct (N × H) |
| 15. C4×Dic202 | C22 | semidirect |
| 19. #15692186 | C22 | semidirect |
| 20. #15692178 | C22 | semidirect |
| 22. C4×#11717579 | C22 | semidirect |
| 32. C2×Dic202 | C2×C4 | semidirect |
| 36. #13108062 | C2×C4 | direct (N × H) |
| 38. C2×#11717579 | C2×C4 | semidirect |
| 73. C2×C4×C101 | SD16 | semidirect |
| 86. Dic202 | C22×C4 | semidirect |
| 88. #11717579 | C22×C4 | semidirect |
| 100. C4×C101 | C2×SD16 | semidirect |
| 106. C2×C101 | C4×SD16 | semidirect |
| 111. C101 | C2×C4×SD16 | semidirect |
| 191. C2×C4 | #13108062 | direct (N × H) |
| 213. C4 | C2×#13108062 | direct (N × H) |
| 217. C2 | C4×#13108062 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C2×C4×Dic202 | 2 |
| C4×#13108062 | 2 |
| C2×#15692186 | 2 |
| C2×#15692178 | 2 |
| C2×#15692176 | 2 |
| C2×C4×#11717579 | 2 |
| C2×C4×D4×C101 | 2 |
| C2×C4×SD16 | 101 |