Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20260690 | C2 | semidirect |
| 4. C2×C8×Dic97 | C2 | semidirect |
| 5. #20260499 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 12. #15690737 | C4 | semidirect |
| 13. #15690734 | C4 | semidirect |
| 14. #15690731 | C4 | semidirect |
| 20. #131×C97 | C4 | semidirect |
| 99. C97 | #1764 | semidirect |
| 109. #131 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690737 | 2 |
| #20260731 | 2 |
| #20260690 | 2 |
| C2×C8×Dic97 | 2 |
| #20260499 | 2 |
| #20260496 | 2 |
| C2×#131×C97 | 2 |
| #1764 | 97 |