Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
270 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#15692190 | C2 | semidirect |
| 3. #20265205 | C2 | semidirect |
| 5. #20264937 | C2 | semidirect |
| 6. #20264932 | C2 | semidirect |
| 19. #15692179 | C4 | semidirect |
| 20. #15692179 | C4 | semidirect |
| 21. #15692176 | C4 | semidirect |
| 22. #15692176 | C4 | semidirect |
| 110. C101 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692262 | 2 |
| C2×#15692190 | 2 |
| #20265205 | 2 |
| #20265173 | 2 |
| #20264937 | 2 |
| #20264932 | 2 |
| C2×#104×C101 | 2 |
| #1866 | 101 |