Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13095511 | C2 | semidirect |
| 2. C22×#13095500 | C2 | semidirect |
| 3. C22×D776 | C2 | semidirect |
| 4. C2×#15690784 | C2 | semidirect |
| 5. #20260882 | C2 | direct (N × H) |
| 6. C2×#15690735 | C2 | semidirect |
| 7. C2×#15690732 | C2 | semidirect |
| 8. C2×C22⋊C8×C97 | C2 | semidirect |
| 12. C2×#13095511 | C22 | semidirect |
| 20. C2×#13095500 | C22 | semidirect |
| 22. C2×D776 | C22 | semidirect |
| 24. #15690784 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 28. #15690732 | C22 | semidirect |
| 32. C22⋊C8×C97 | C22 | semidirect |
| 40. C2×Dic194 | D4 | semidirect |
| 47. C2×D388 | D4 | semidirect |
| 107. D388 | C2×D4 | semidirect |
| 111. Dic194 | C2×D4 | semidirect |
| 137. C2×C97 | #449 | semidirect |
| 144. C97 | C2×#449 | semidirect |
| 152. C2×C22⋊C8 | D97 | semidirect |
| 176. C22⋊C8 | C2×D97 | semidirect |
| 283. C2 | #20260882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C22×#13095500 | 2 |
| C22×D776 | 2 |
| C2×#15690784 | 2 |
| #20260882 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| C2×C22⋊C8×C97 | 2 |
| C2×#449 | 97 |