Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×D776 | C2 | semidirect |
| 2. C22×#13095494 | C2 | semidirect |
| 3. C2×#15690785 | C2 | semidirect |
| 4. #20260989 | C2 | direct (N × H) |
| 5. C2×#15690730 | C2 | semidirect |
| 6. C2×#106×C97 | C2 | semidirect |
| 11. C2×D776 | C22 | semidirect |
| 13. C2×#13095494 | C22 | semidirect |
| 16. #15690785 | C22 | semidirect |
| 18. #15690730 | C22 | semidirect |
| 21. #106×C97 | C22 | semidirect |
| 42. C2×C8×C97 | D4 | semidirect |
| 69. C8×C97 | C2×D4 | semidirect |
| 86. C2×C97 | #469 | semidirect |
| 92. C97 | C2×#469 | semidirect |
| 97. C2×#106 | D97 | semidirect |
| 112. #106 | C2×D97 | semidirect |
| 133. C2×C8 | D388 | semidirect |
| 162. C8 | C2×D388 | semidirect |
| 180. C2 | #20260989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C22×#13095494 | 2 |
| C2×#15690785 | 2 |
| #20260989 | 2 |
| C2×#15690730 | 2 |
| C2×#106×C97 | 2 |
| C2×#469 | 97 |