Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #20265218 | C2 | direct (N × H) |
| 5. C2×#15692188 | C2 | semidirect |
| 6. C2×#15692187 | C2 | semidirect |
| 7. C2×#15692186 | C2 | semidirect |
| 8. C2×#107×C101 | C2 | semidirect |
| 11. C2×#13108057 | C4 | semidirect |
| 23. #15692188 | C22 | semidirect |
| 24. #15692187 | C22 | semidirect |
| 25. #15692186 | C22 | semidirect |
| 29. #107×C101 | C22 | semidirect |
| 40. #13108057 | C2×C4 | semidirect |
| 41. C2×#11717579 | C2×C4 | semidirect |
| 53. C2×C8×C101 | C2×C4 | semidirect |
| 82. C8×C101 | C22×C4 | semidirect |
| 83. #11717579 | C22×C4 | semidirect |
| 100. C2×C101 | #428 | semidirect |
| 106. C101 | C2×#428 | semidirect |
| 112. C2×#107 | D101 | semidirect |
| 133. #107 | C2×D101 | semidirect |
| 152. C2×C8 | C4×D101 | semidirect |
| 189. C8 | C2×C4×D101 | semidirect |
| 207. C2 | #20265218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108057 | 2 |
| C2×#15692213 | 2 |
| C2×C4⋊C4×D101 | 2 |
| #20265218 | 2 |
| C2×#15692188 | 2 |
| C2×#15692187 | 2 |
| C2×#15692186 | 2 |
| C2×#107×C101 | 2 |
| C2×#428 | 101 |