Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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×#13095500 | C2 | semidirect |
| 3. C2×#15690798 | C2 | semidirect |
| 4. C2×C4×D388 | C2 | semidirect |
| 5. #20260951 | C2 | direct (N × H) |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#15690732 | C2 | semidirect |
| 8. C2×C4⋊C8×C97 | C2 | semidirect |
| 14. C2×#13095500 | C22 | semidirect |
| 18. #15690798 | C22 | semidirect |
| 20. C4×D388 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 30. C4⋊C8×C97 | C22 | semidirect |
| 117. C2×C97 | #463 | semidirect |
| 124. C97 | C2×#463 | semidirect |
| 130. C2×C4⋊C8 | D97 | semidirect |
| 152. C4⋊C8 | C2×D97 | semidirect |
| 243. C2 | #20260951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C22×D776 | 2 |
| C2×#15690798 | 2 |
| C2×C4×D388 | 2 |
| #20260951 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C2×C4⋊C8×C97 | 2 |
| C2×#463 | 97 |