Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #20261759 | C2 | semidirect |
| 2. #20261758 | C2 | semidirect |
| 3. #20261754 | C2 | semidirect |
| 4. #20261742 | C2 | semidirect |
| 7. #20261700 | C2 | semidirect |
| 11. #15690877 | C22 | semidirect |
| 12. C4⋊#11715897 | C22 | semidirect |
| 18. #15690865 | C22 | semidirect |
| 19. C4×#11715897 | C22 | semidirect |
| 111. C97 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261759 | 2 |
| #20261758 | 2 |
| #20261754 | 2 |
| #20261742 | 2 |
| #20261706 | 2 |
| #20261703 | 2 |
| #20261700 | 2 |
| #117×D97 | 2 |
| #2924 | 97 |