Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #20266192 | C2 | semidirect |
| 4. M16×#87938 | C2 | semidirect |
| 5. #20266060 | C2 | semidirect |
| 6. #20266049 | C2 | semidirect |
| 23. #15692174 | C4 | semidirect |
| 24. #15692171 | C4 | semidirect |
| 25. #15692171 | C4 | semidirect |
| 26. #101×C101 | C4 | semidirect |
| 106. C101 | #1932 | semidirect |
| 128. #101 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266192 | 2 |
| #20266176 | 2 |
| C2×#15692320 | 2 |
| M16×#87938 | 2 |
| #20266060 | 2 |
| #20266049 | 2 |
| #20265160 | 2 |
| #1932 | 101 |