Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #20266184 | C2 | semidirect |
| 4. C2×C8×#87938 | C2 | semidirect |
| 5. #20266053 | C2 | semidirect |
| 6. #20266047 | C2 | semidirect |
| 21. #15692180 | C4 | semidirect |
| 22. #15692178 | C4 | semidirect |
| 23. #15692176 | C4 | semidirect |
| 24. #102×C101 | C4 | semidirect |
| 106. C101 | #1937 | semidirect |
| 127. #102 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266184 | 2 |
| C2×#15692319 | 2 |
| #20266151 | 2 |
| C2×C8×#87938 | 2 |
| #20266053 | 2 |
| #20266047 | 2 |
| #20265170 | 2 |
| #1937 | 101 |