Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 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. #20261760 | C2 | semidirect |
| 2. #20261759 | C2 | semidirect |
| 3. #20261740 | C2 | semidirect |
| 4. #20261739 | C2 | semidirect |
| 6. C4×#13095521 | C2 | semidirect |
| 10. #15690877 | C22 | semidirect |
| 11. C4⋊#11715897 | C22 | semidirect |
| 14. #15690865 | C22 | semidirect |
| 15. C4×#11715897 | C22 | semidirect |
| 105. C97 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261760 | 2 |
| #20261759 | 2 |
| #20261740 | 2 |
| #20261739 | 2 |
| #20261706 | 2 |
| C4×#13095521 | 2 |
| #117×D97 | 2 |
| #2921 | 97 |