Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
464 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20261770 | C2 | semidirect |
| 2. #20261766 | C2 | semidirect |
| 3. D4×#11715897 | C2 | semidirect |
| 4. #20261756 | C2 | semidirect |
| 5. #20261752 | C2 | semidirect |
| 6. #20261705 | C2 | semidirect |
| 7. C2×C22⋊#11715897 | C2 | semidirect |
| 9. C2×#13095520 | C22 | semidirect |
| 10. C22×#11715897 | C22 | semidirect |
| 11. #15690877 | C22 | semidirect |
| 12. C4⋊#11715897 | C22 | semidirect |
| 16. C22⋊#11715897 | C22 | semidirect |
| 17. C22⋊#11715897 | C22 | semidirect |
| 18. #15690865 | C22 | semidirect |
| 19. C4×#11715897 | C22 | semidirect |
| 69. D4×C97 | M16 | semidirect |
| 115. C97 | #2974 | semidirect |
| 184. D4 | #13095520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261770 | 2 |
| #20261766 | 2 |
| D4×#11715897 | 2 |
| #20261756 | 2 |
| #20261752 | 2 |
| #20261705 | 2 |
| C2×C22⋊#11715897 | 2 |
| C2×D4×Dic97 | 2 |
| #2974 | 97 |