Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
464 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 166 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. #20266211 | C2 | semidirect |
| 2. #20266206 | C2 | semidirect |
| 3. D4×#11717581 | C2 | semidirect |
| 4. #20266199 | C2 | semidirect |
| 5. #20266196 | C2 | semidirect |
| 6. #20266148 | C2 | semidirect |
| 7. C2×#15692312 | C2 | semidirect |
| 9. C2×#13108084 | C22 | semidirect |
| 10. C22×#11717581 | C22 | semidirect |
| 11. C4⋊#11717581 | C22 | semidirect |
| 12. C4⋊#11717581 | C22 | semidirect |
| 16. #15692312 | C22 | semidirect |
| 17. C22⋊#11717581 | C22 | semidirect |
| 18. #15692310 | C22 | semidirect |
| 19. C4×#11717581 | C22 | semidirect |
| 67. D4×C101 | M16 | semidirect |
| 115. C101 | #2974 | semidirect |
| 184. D4 | #13108084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266211 | 2 |
| #20266206 | 2 |
| D4×#11717581 | 2 |
| #20266199 | 2 |
| #20266196 | 2 |
| #20266148 | 2 |
| C2×#15692312 | 2 |
| C4×D4×D101 | 2 |
| #2974 | 101 |