Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×Dic202 | C2 | semidirect |
| 3. C2×#15692288 | C2 | direct (N × H) |
| 4. C22×Dic404 | C2 | semidirect |
| 5. C22×#13108063 | C2 | semidirect |
| 6. C22×M16×C101 | C2 | semidirect |
| 13. C22×Dic202 | C22 | semidirect |
| 18. #15692288 | C22 | direct (N × H) |
| 19. C2×Dic404 | C22 | semidirect |
| 20. C2×#13108063 | C22 | semidirect |
| 22. C2×M16×C101 | C22 | semidirect |
| 33. C2×Dic202 | C23 | semidirect |
| 41. Dic404 | C23 | semidirect |
| 42. #13108063 | C23 | semidirect |
| 48. M16×C101 | C23 | semidirect |
| 74. C22×C101 | #137 | semidirect |
| 85. C2×C101 | C2×#137 | semidirect |
| 89. C101 | C22×#137 | semidirect |
| 95. C22×M16 | D101 | semidirect |
| 111. C2×M16 | C2×D101 | semidirect |
| 137. M16 | C22×D101 | semidirect |
| 165. C22 | #15692288 | direct (N × H) |
| 175. C2 | C2×#15692288 | 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 |
| C23×Dic202 | 2 |
| C2×#15692288 | 2 |
| C22×Dic404 | 2 |
| C22×#13108063 | 2 |
| C22×M16×C101 | 2 |
| C22×#137 | 101 |