Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#15690889 | C2 | semidirect |
| 2. #20261715 | C2 | direct (N × H) |
| 3. C2×#15690868 | C2 | semidirect |
| 6. #15690889 | C22 | semidirect |
| 10. #15690868 | C22 | semidirect |
| 14. C2×#13095510 | C4 | semidirect |
| 16. C22×Dic194 | C4 | semidirect |
| 18. C23×Dic97 | C4 | semidirect |
| 20. C22×D4×C97 | C4 | semidirect |
| 33. C2×Dic194 | C2×C4 | semidirect |
| 43. C22×Dic97 | C2×C4 | semidirect |
| 52. C2×D4×C97 | C2×C4 | semidirect |
| 108. C2×C97 | #410 | semidirect |
| 113. C97 | C2×#410 | semidirect |
| 125. C22×D4 | #87604 | semidirect |
| 149. C2×D4 | C2×#87604 | semidirect |
| 223. C2 | #20261715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261715 | 2 |
| C2×#15690868 | 2 |
| C22×#13095510 | 2 |
| C2×#410 | 97 |