Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261036 | C2 | semidirect |
| 4. #20261036 | C2 | semidirect |
| 5. #20261026 | C2 | semidirect |
| 6. #20261016 | C2 | semidirect |
| 7. #20260777 | C2 | semidirect |
| 8. #20260773 | C2 | semidirect |
| 11. #424×C97 | C2 | semidirect |
| 13. #15690810 | C22 | semidirect |
| 15. #15690802 | C22 | semidirect |
| 26. #15690744 | C22 | semidirect |
| 27. #15690744 | C22 | semidirect |
| 28. #15690744 | C22 | semidirect |
| 29. #15690742 | C22 | semidirect |
| 30. #15690742 | C22 | semidirect |
| 31. #15690742 | C22 | semidirect |
| 39. C4⋊C8×C97 | C22 | semidirect |
| 40. C4⋊C8×C97 | C22 | semidirect |
| 45. C2×D388 | Q8 | semidirect |
| 125. C97 | #3081 | semidirect |
| 134. #424 | D97 | semidirect |
| 160. C4⋊C8 | C2×D97 | semidirect |
| 161. C4⋊C8 | 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 |
| #20261036 | 2 |
| #20261026 | 2 |
| #20261016 | 2 |
| #20260777 | 2 |
| #20260773 | 2 |
| #20260741 | 2 |
| C2×#15690732 | 2 |
| #424×C97 | 2 |
| #3081 | 97 |