Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D97 | C2 | semidirect |
| 3. C2×#15690786 | C2 | semidirect |
| 4. #20260990 | C2 | semidirect |
| 5. #20260978 | C2 | semidirect |
| 6. #20260973 | C2 | semidirect |
| 7. #20260961 | C2 | semidirect |
| 8. #20260777 | C2 | semidirect |
| 9. #20260744 | C2 | semidirect |
| 10. #20260736 | C2 | semidirect |
| 11. C2×#137×C97 | C2 | semidirect |
| 33. #15690744 | C22 | semidirect |
| 34. #15690742 | C22 | semidirect |
| 35. #15690734 | C22 | semidirect |
| 36. #15690734 | C22 | semidirect |
| 37. #15690734 | C22 | semidirect |
| 38. #15690731 | C22 | semidirect |
| 42. C2×Q16×C97 | C22 | semidirect |
| 43. C2×SD16×C97 | C22 | semidirect |
| 90. M16×C97 | D4 | semidirect |
| 145. C2×D97 | #137 | semidirect |
| 164. C97 | #3056 | semidirect |
| 165. C2×#137 | D97 | semidirect |
| 180. C2×Q16 | C2×D97 | semidirect |
| 181. C2×SD16 | C2×D97 | semidirect |
| 236. M16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D97 | 2 |
| #20261242 | 2 |
| C2×#15690786 | 2 |
| #20260990 | 2 |
| #20260978 | 2 |
| #20260973 | 2 |
| #20260961 | 2 |
| #20260777 | 2 |
| #20260744 | 2 |
| #20260736 | 2 |
| C2×#137×C97 | 2 |
| #3056 | 97 |