Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4×Dic101 | C2 | semidirect |
| 3. C2×#15692181 | C2 | direct (N × H) |
| 4. C22×M16×C101 | C2 | semidirect |
| 7. C2×#13108074 | C4 | semidirect |
| 9. C22×Dic202 | C4 | semidirect |
| 10. C22×D404 | C4 | semidirect |
| 15. C2×C4×Dic101 | C22 | semidirect |
| 16. #15692181 | C22 | direct (N × H) |
| 19. C2×M16×C101 | C22 | semidirect |
| 25. #13108074 | C2×C4 | semidirect |
| 28. C2×Dic202 | C2×C4 | semidirect |
| 30. C2×D404 | C2×C4 | semidirect |
| 39. C4×Dic101 | C23 | semidirect |
| 48. M16×C101 | C23 | semidirect |
| 71. D404 | C22×C4 | semidirect |
| 75. Dic202 | C22×C4 | semidirect |
| 79. C22×C101 | #104 | semidirect |
| 93. C2×C101 | C2×#104 | semidirect |
| 97. C101 | C22×#104 | semidirect |
| 99. C22×M16 | D101 | semidirect |
| 113. C2×M16 | C2×D101 | semidirect |
| 143. M16 | C22×D101 | semidirect |
| 178. C22 | #15692181 | direct (N × H) |
| 191. C2 | C2×#15692181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C22×C4×Dic101 | 2 |
| C2×#15692181 | 2 |
| C22×M16×C101 | 2 |
| C22×#104 | 101 |