Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20261445 | C2 | semidirect |
| 2. #20261099 | C2 | semidirect |
| 3. #20261081 | C2 | semidirect |
| 4. #20261035 | C2 | semidirect |
| 5. #20261025 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260927 | C2 | semidirect |
| 8. #20260866 | C2 | semidirect |
| 9. #20260845 | C2 | semidirect |
| 10. C4×#13095496 | C2 | semidirect |
| 11. #550×C97 | C2 | semidirect |
| 97. D388 | #41 | semidirect |
| 130. C97 | #3366 | semidirect |
| 132. #550 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261445 | 2 |
| #20261099 | 2 |
| #20261081 | 2 |
| #20261035 | 2 |
| #20261025 | 2 |
| #20260927 | 2 |
| #20260866 | 2 |
| #20260845 | 2 |
| C4×#13095496 | 2 |
| #550×C97 | 2 |
| #3366 | 97 |