Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261363 | C2 | semidirect |
| 3. #20261038 | C2 | semidirect |
| 4. #20261034 | C2 | semidirect |
| 5. #20261024 | C2 | semidirect |
| 6. #20261014 | C2 | semidirect |
| 7. #20260778 | C2 | semidirect |
| 8. #20260761 | C2 | semidirect |
| 11. #427×C97 | C2 | semidirect |
| 15. #15690809 | C22 | semidirect |
| 17. #15690801 | C22 | semidirect |
| 26. #15690743 | C22 | semidirect |
| 27. #15690741 | C22 | semidirect |
| 28. #15690739 | C22 | semidirect |
| 29. #15690739 | C22 | semidirect |
| 37. #107×C97 | C22 | semidirect |
| 38. #107×C97 | C22 | semidirect |
| 39. #106×C97 | C22 | semidirect |
| 40. #106×C97 | C22 | semidirect |
| 45. C2×D388 | Q8 | semidirect |
| 125. C97 | #3081 | semidirect |
| 133. #427 | D97 | semidirect |
| 155. #107 | C2×D97 | semidirect |
| 156. #107 | C2×D97 | semidirect |
| 158. #106 | C2×D97 | semidirect |
| 159. #106 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261209 | 2 |
| #20261038 | 2 |
| #20261034 | 2 |
| #20261024 | 2 |
| #20261014 | 2 |
| #20260778 | 2 |
| #20260761 | 2 |
| #20260739 | 2 |
| C2×#15690732 | 2 |
| #427×C97 | 2 |
| #3081 | 97 |