Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 162 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. #20261736 | C2 | semidirect |
| 5. #20261694 | C2 | semidirect |
| 6. C4×#13095519 | C2 | semidirect |
| 10. #15690877 | C22 | semidirect |
| 11. C4⋊#11715897 | C22 | semidirect |
| 14. #15690865 | C22 | semidirect |
| 15. C4×#11715897 | C22 | semidirect |
| 98. D97 | #433 | semidirect |
| 100. C97 | C2×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261760 | 2 |
| #20261759 | 2 |
| #20261736 | 2 |
| #20261703 | 2 |
| #20261694 | 2 |
| C4×#13095519 | 2 |
| #117×D97 | 2 |
| C2×#433 | 97 |