Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#15692254 | C2 | semidirect |
| 3. #20265466 | C2 | direct (N × H) |
| 4. C2×#15692186 | C2 | semidirect |
| 5. C2×#15692184 | C2 | semidirect |
| 8. C2×#106×C101 | C2 | semidirect |
| 14. #15692254 | C22 | semidirect |
| 21. #15692186 | C22 | semidirect |
| 22. #15692184 | C22 | semidirect |
| 28. #106×C101 | C22 | semidirect |
| 34. C2×D404 | Q8 | semidirect |
| 79. D404 | C2×Q8 | semidirect |
| 100. C2×C101 | #476 | semidirect |
| 106. C101 | C2×#476 | semidirect |
| 111. C2×#106 | D101 | semidirect |
| 131. #106 | C2×D101 | semidirect |
| 207. C2 | #20265466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| C2×#15692217 | 2 |
| #20265466 | 2 |
| C2×#15692186 | 2 |
| C2×#15692184 | 2 |
| C2×#15692177 | 2 |
| C2×#15692175 | 2 |
| C2×#106×C101 | 2 |
| C2×#476 | 101 |