Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 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 |
|---|---|---|
| 1. #20265803 | C2 | direct (N × H) |
| 2. C2×#15692234 | C2 | semidirect |
| 3. C2×#15692232 | C2 | semidirect |
| 6. C22×Dic202 | C22 | semidirect |
| 8. #15692234 | C22 | semidirect |
| 9. #15692232 | C22 | semidirect |
| 10. C2×C4⋊Dic101 | C22 | semidirect |
| 11. C2×#13108053 | C22 | semidirect |
| 20. C2×Dic202 | C23 | semidirect |
| 24. C4⋊Dic101 | C23 | semidirect |
| 25. #13108053 | C23 | semidirect |
| 29. C24×C101 | Q8 | semidirect |
| 43. C23×C101 | C2×Q8 | semidirect |
| 68. C2×C101 | #543 | semidirect |
| 72. C101 | C2×#543 | semidirect |
| 92. C24 | Dic202 | semidirect |
| 115. C23 | C2×Dic202 | semidirect |
| 140. C2 | #20265803 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265803 | 2 |
| C2×#15692234 | 2 |
| C2×#15692232 | 2 |
| C22×C22⋊Dic101 | 2 |
| C22×C22⋊C4×C101 | 2 |
| C2×#543 | 101 |