Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690857 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. #20261302 | C2 | semidirect |
| 4. #20260877 | C2 | semidirect |
| 5. #20260872 | C2 | semidirect |
| 6. #20260745 | C2 | semidirect |
| 7. #20260731 | C2 | semidirect |
| 8. #20260703 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 15. C2×#13095510 | C22 | semidirect |
| 18. C2×Q8×D97 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 28. #15690734 | C22 | semidirect |
| 29. #15690731 | C22 | semidirect |
| 30. #15690722 | C22 | semidirect |
| 48. C2×Dic194 | D4 | semidirect |
| 69. #41×C97 | D4 | semidirect |
| 146. C97 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D97 | semidirect |
| 191. #41 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| C22×#13095499 | 2 |
| #20261302 | 2 |
| #20260877 | 2 |
| #20260872 | 2 |
| #20260745 | 2 |
| #20260731 | 2 |
| #20260703 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3010 | 97 |