Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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. #20261769 | C2 | semidirect |
| 2. #20261764 | C2 | semidirect |
| 3. D4×#11715897 | C2 | semidirect |
| 4. #20261757 | C2 | semidirect |
| 5. #20261754 | C2 | semidirect |
| 6. #20261706 | C2 | semidirect |
| 7. C2×#15690867 | C2 | semidirect |
| 9. C2×#13095521 | C22 | semidirect |
| 10. C22×#11715897 | C22 | semidirect |
| 11. C4⋊#11715897 | C22 | semidirect |
| 12. C4⋊#11715897 | C22 | semidirect |
| 16. #15690867 | C22 | semidirect |
| 17. C22⋊#11715897 | C22 | semidirect |
| 18. #15690865 | C22 | semidirect |
| 19. C4×#11715897 | C22 | semidirect |
| 67. D4×C97 | M16 | semidirect |
| 115. C97 | #2974 | semidirect |
| 184. D4 | #13095521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261769 | 2 |
| #20261764 | 2 |
| D4×#11715897 | 2 |
| #20261757 | 2 |
| #20261754 | 2 |
| #20261706 | 2 |
| C2×#15690867 | 2 |
| C4×D4×D97 | 2 |
| #2974 | 97 |