Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20265506 | C2 | direct (N × H) |
| 4. C2×#15692187 | C2 | semidirect |
| 5. C2×#15692186 | C2 | semidirect |
| 6. C2×#15692179 | C2 | semidirect |
| 8. C2×#103×C101 | C2 | semidirect |
| 21. #15692187 | C22 | semidirect |
| 22. #15692186 | C22 | semidirect |
| 23. #15692179 | C22 | semidirect |
| 28. #103×C101 | C22 | semidirect |
| 103. C2×C101 | #483 | semidirect |
| 109. C101 | C2×#483 | semidirect |
| 116. C2×#103 | D101 | semidirect |
| 136. #103 | C2×D101 | semidirect |
| 213. C2 | #20265506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692231 | 2 |
| C2×C4⋊C4×D101 | 2 |
| #20265506 | 2 |
| C2×#15692187 | 2 |
| C2×#15692186 | 2 |
| C2×#15692179 | 2 |
| C2×#15692167 | 2 |
| C2×#103×C101 | 2 |
| C2×#483 | 101 |