Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#13095500 | C2 | semidirect |
| 2. C2×#15690816 | C2 | semidirect |
| 3. #20261311 | C2 | semidirect |
| 5. #20260982 | C2 | semidirect |
| 6. #20260965 | C2 | semidirect |
| 7. #20260743 | C2 | semidirect |
| 8. #20260739 | C2 | semidirect |
| 9. #427×C97 | C2 | semidirect |
| 18. C2×#13095494 | C22 | semidirect |
| 19. C2×C8×D97 | C22 | semidirect |
| 25. #15690790 | C22 | semidirect |
| 28. #15690733 | C22 | semidirect |
| 33. #107×C97 | C22 | semidirect |
| 34. #106×C97 | C22 | semidirect |
| 62. C2×C8×C97 | D4 | semidirect |
| 121. C97 | #3057 | semidirect |
| 128. #427 | D97 | semidirect |
| 152. #107 | C2×D97 | semidirect |
| 153. #106 | C2×D97 | semidirect |
| 180. C2×C8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×#15690816 | 2 |
| #20261311 | 2 |
| #20261304 | 2 |
| #20260982 | 2 |
| #20260965 | 2 |
| #20260743 | 2 |
| #20260739 | 2 |
| #427×C97 | 2 |
| #3057 | 97 |