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×#13095510 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. C2×#15690781 | C2 | semidirect |
| 4. #20260877 | C2 | direct (N × H) |
| 5. C2×#15690735 | C2 | semidirect |
| 6. C2×#15690731 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C22×D8×C97 | C2 | semidirect |
| 12. C2×#13095510 | C22 | semidirect |
| 19. C2×#13095499 | C22 | semidirect |
| 22. #15690781 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690731 | C22 | semidirect |
| 27. #15690722 | C22 | semidirect |
| 31. C2×D8×C97 | C22 | semidirect |
| 39. C2×Dic194 | D4 | semidirect |
| 67. C2×D4×C97 | D4 | semidirect |
| 92. D4×C97 | C2×D4 | semidirect |
| 111. Dic194 | C2×D4 | semidirect |
| 138. C2×C97 | #449 | semidirect |
| 144. C97 | C2×#449 | semidirect |
| 147. C22×D8 | D97 | semidirect |
| 167. C2×D8 | C2×D97 | semidirect |
| 196. C2×D4 | C22⋊D97 | semidirect |
| 241. D4 | C2×C22⋊D97 | semidirect |
| 283. C2 | #20260877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095510 | 2 |
| C22×#13095499 | 2 |
| C2×#15690781 | 2 |
| #20260877 | 2 |
| C2×#15690735 | 2 |
| C2×#15690731 | 2 |
| C2×#15690722 | 2 |
| C22×D8×C97 | 2 |
| C2×#449 | 97 |