Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20265023 | C2 | semidirect |
| 4. #20264938 | C2 | semidirect |
| 5. C4×M16×C101 | C2 | semidirect |
| 7. C4×Dic202 | C4 | semidirect |
| 8. C4×D404 | C4 | semidirect |
| 14. #15692181 | C4 | semidirect |
| 35. C4×Dic101 | C2×C4 | semidirect |
| 39. M16×C101 | C2×C4 | semidirect |
| 83. C101 | #1759 | semidirect |
| 86. C4×M16 | D101 | semidirect |
| 114. M16 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13108074 | 2 |
| C2×#15692181 | 2 |
| #20265023 | 2 |
| #20264938 | 2 |
| C4×M16×C101 | 2 |
| #1759 | 101 |