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×#15690843 | C2 | semidirect |
| 2. C2×#15690818 | C2 | semidirect |
| 4. #20261311 | C2 | semidirect |
| 5. #20260994 | C2 | semidirect |
| 6. #20260982 | C2 | semidirect |
| 7. #20260977 | C2 | semidirect |
| 8. #20260965 | C2 | semidirect |
| 9. #20260729 | C2 | semidirect |
| 10. C2×#15690733 | C2 | semidirect |
| 11. #428×C97 | C2 | semidirect |
| 77. M16×C97 | D4 | semidirect |
| 144. C97 | #3063 | semidirect |
| 153. #428 | D97 | semidirect |
| 210. M16 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| C2×#15690818 | 2 |
| #20261316 | 2 |
| #20261311 | 2 |
| #20260994 | 2 |
| #20260982 | 2 |
| #20260977 | 2 |
| #20260965 | 2 |
| #20260729 | 2 |
| C2×#15690733 | 2 |
| #428×C97 | 2 |
| #3063 | 97 |