Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #20266143 | C2 | semidirect |
| 4. #20266060 | C2 | semidirect |
| 9. C2×#13108083 | C4 | semidirect |
| 11. C22×#11717581 | C4 | semidirect |
| 18. #15692173 | C4 | semidirect |
| 19. #15692172 | C4 | semidirect |
| 20. #100×C101 | C4 | semidirect |
| 78. C101 | #1757 | semidirect |
| 95. #100 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692342 | 2 |
| #20266157 | 2 |
| #20266143 | 2 |
| #20266060 | 2 |
| #20265158 | 2 |
| #1757 | 101 |