Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690841 | C2 | semidirect |
| 3. #20261215 | C2 | semidirect |
| 4. #20260954 | C2 | semidirect |
| 5. #20260947 | C2 | semidirect |
| 6. #20260942 | C2 | semidirect |
| 7. #20260937 | C2 | semidirect |
| 8. #20260762 | C2 | semidirect |
| 9. #20260736 | C2 | semidirect |
| 10. C2×#15690734 | C2 | semidirect |
| 11. #536×C97 | C2 | semidirect |
| 147. C97 | #3046 | semidirect |
| 150. #536 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| C2×#15690830 | 2 |
| #20261215 | 2 |
| #20260954 | 2 |
| #20260947 | 2 |
| #20260942 | 2 |
| #20260937 | 2 |
| #20260762 | 2 |
| #20260736 | 2 |
| C2×#15690734 | 2 |
| #536×C97 | 2 |
| #3046 | 97 |