Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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. #20266188 | C2 | semidirect |
| 4. #20266049 | C2 | semidirect |
| 17. #15692172 | C4 | semidirect |
| 18. #15692171 | C4 | semidirect |
| 19. #100×C101 | C4 | semidirect |
| 38. #13108058 | C2×C4 | semidirect |
| 42. M16×C101 | C2×C4 | semidirect |
| 94. C101 | #1856 | semidirect |
| 113. #100 | #87938 | semidirect |
| 127. M16 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266244 | 2 |
| #20266188 | 2 |
| #20266129 | 2 |
| #20266049 | 2 |
| #100×D101 | 2 |
| #1856 | 101 |