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×#15690840 | C2 | semidirect |
| 2. C2×#15690817 | C2 | semidirect |
| 3. #20261306 | C2 | semidirect |
| 4. #20260991 | C2 | semidirect |
| 5. #20260979 | C2 | semidirect |
| 6. #20260974 | C2 | semidirect |
| 7. #20260962 | C2 | semidirect |
| 8. #20260775 | C2 | semidirect |
| 9. #20260731 | C2 | semidirect |
| 10. C2×#15690733 | C2 | semidirect |
| 51. #13095495 | D4 | semidirect |
| 144. C97 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690817 | 2 |
| #20261306 | 2 |
| #20260991 | 2 |
| #20260979 | 2 |
| #20260974 | 2 |
| #20260962 | 2 |
| #20260775 | 2 |
| #20260731 | 2 |
| C2×#15690733 | 2 |
| #537×C97 | 2 |
| #3063 | 97 |