Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #41×Dic97 | C2 | semidirect |
| 3. #20260751 | C2 | semidirect |
| 4. C2×#15690736 | C2 | semidirect |
| 5. #568×C97 | C2 | semidirect |
| 7. #15690857 | C4 | semidirect |
| 8. #15690856 | C4 | semidirect |
| 14. #15690769 | C22 | semidirect |
| 15. C2×C4×Dic97 | C22 | semidirect |
| 16. #15690736 | C22 | semidirect |
| 17. #15690736 | C22 | semidirect |
| 20. C2×M16×C97 | C22 | semidirect |
| 24. #13095511 | C2×C4 | semidirect |
| 27. C2×Dic194 | C2×C4 | semidirect |
| 29. C2×D388 | C2×C4 | semidirect |
| 84. C97 | #2901 | semidirect |
| 86. #568 | D97 | semidirect |
| 98. C2×M16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261571 | 2 |
| #41×Dic97 | 2 |
| #20260751 | 2 |
| C2×#15690736 | 2 |
| #568×C97 | 2 |
| #2901 | 97 |