Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #20261218 | C2 | semidirect |
| 3. #20260741 | C2 | semidirect |
| 4. #20260737 | C2 | semidirect |
| 5. #20260732 | C2 | semidirect |
| 6. C2×#15690732 | C2 | semidirect |
| 7. C2×#131×C97 | C2 | semidirect |
| 9. #15690856 | C4 | semidirect |
| 16. #15690769 | C22 | semidirect |
| 17. C2×C4⋊Dic97 | C22 | semidirect |
| 18. #15690735 | C22 | semidirect |
| 19. #15690735 | C22 | semidirect |
| 20. #15690732 | C22 | semidirect |
| 21. #15690732 | C22 | semidirect |
| 22. #15690732 | C22 | semidirect |
| 25. C2×M16×C97 | C22 | semidirect |
| 26. C22×C8×C97 | C22 | semidirect |
| 30. #13095511 | C2×C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 98. C97 | #2897 | semidirect |
| 100. C2×#131 | D97 | semidirect |
| 114. C2×M16 | C2×D97 | semidirect |
| 115. C22×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690856 | 2 |
| #20261218 | 2 |
| #20260741 | 2 |
| #20260737 | 2 |
| #20260732 | 2 |
| C2×#15690732 | 2 |
| C2×#131×C97 | 2 |
| #2897 | 97 |